Physics Book - Recent changes [en]

Loop Rule

Ss87 — Thu, 30 Apr 2026 19:05:09 GMT

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-'''Claimed by Aazam Alam (Fall 2025)'''
+'''Last edit by Shlesh Sakpal (Spring 2026)'''
 The Loop Rule, also known as Kirchhoff's Second Law, is a fundamental principle of electric circuits which states that the sum of potential differences around a closed circuit is equal to zero. More simply, when you travel around an entire circuit loop, you will return to the starting voltage. Note that is only true when the magnetic field is neither fluctuating nor time varying. If a changing magnetic field links the closed loop, then the principle of energy conservation does not apply to the electric field, causing the Loop Rule to be inaccurate in this scenario.
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 LOOP 3: <math> emf - I_2R_2 = 0 </math>
 ===A Mathematical Model===

Rolling Motion

Jfredeman6 — Thu, 30 Apr 2026 13:59:52 GMT

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	==== Comparison of Slipping vs. Non-Slipping Motion ====		==== Comparison of Slipping vs. Non-Slipping Motion ====
	'''James Fredeman – Spring 2026'''		'''James Fredeman – Spring 2026'''
	The following simulation demonstrates the dynamics of two objects—one rolling ~~without slipping~~ and one experiencing kinetic friction—as they move up and down an incline.		The following simulation demonstrates the dynamics of two objects—one slipping without rolling and one experiencing kinetic friction—as they move up and down an incline.

	View Simulation: [https://trinket.io/glowscript/24b2cde21471 ~~Interactive Rolling~~ vs. Slipping Model]		View Simulation: [https://trinket.io/glowscript/24b2cde21471 slipping vs. Slipping into Rolling Model]

	* Scenario A: Constrained No-Slip		* Scenario A: Constrained No-Slip

Translational, Rotational and Vibrational Energy

Slakshmisha3 — Wed, 29 Apr 2026 04:14:47 GMT

References

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	====Moment of Inertia====		====Moment of Inertia====
	\[
	I = \sum ~~m_ir_i~~^2		::<math>I = \sum m_i r_i^2</math>
	\]

	This measures how difficult it is to rotate an object.		This measures how difficult it is to rotate an object.
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	Mass farther from the axis increases rotational energy because of the \(r^2\) term.		Mass farther from the axis increases rotational energy because of the \(r^2\) term.

	[[File:~~Moment_of_inertia_diagram~~.svg\|~~300px\|right\|thumb\|Mass farther from the axis increases rotational inertia.~~]]
			[[File:Moment of inertia solid sphere.svg\|Moment_of_inertia_solid_sphere]]

	---		---
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	=====Angular Speed and Velocity=====		=====Angular Speed and Velocity=====

	\[		::<math>\omega = \cfrac{2\pi}{T}</math>
	\omega = \~~frac~~{2\pi}{T}
	\]

	\[		::<math>v = \omega r</math>
	v = \omega r
	\]

	Points farther from the center move faster.		Points farther from the center move faster.
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	Given:		Given:
	* \(m = 2 \, kg\)		* <math>m = 2 \, kg</math>
	* \(v = 3 \, m/~~s\)~~		* <math>v = 3 \, \frac{m}{s}</math>
	* \(I = \~~frac~~{1}{2}mr^2\)		* <math>I = \cfrac{1}{2}mr^2</math>

	Step 1: Translational Energy		Step 1: Translational Energy

	\[		::<math>K_{trans} = \cfrac{1}{2}mv^2 = 9 \, J</math>
	K_{trans} = \~~frac~~{1}{2}mv^2 = 9 \, J
	\]

	Step 2: Rotational Energy		Step 2: Rotational Energy

	\[ K_{~~rot~~} = \~~frac~~{1}{2}~~I\omega~~^2		::<math>K_{trans} = \cfrac{1}{2}mv^2 = 9 \, J</math>
	\]

	Using \( \omega = \~~frac~~{v}{r} \): \[ K_{rot} = \~~frac~~{1}{4}mv^2 = 4.5 \, J \]		Using <math>\omega = \cfrac{v}{r}</math>:

			::<math>K_{rot} = \cfrac{1}{4}mv^2 = 4.5 \, J</math>

	Total Energy:		Total Energy:

	\[ K_{total} = 13.5 \, J		::<math>K_{total} = 13.5 \, J</math>
	\]

	---		---
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	Kinetic energy in real systems consists of multiple components. By separating it into translational, rotational, and vibrational parts, we can more accurately understand and analyze motion.		Kinetic energy in real systems consists of multiple components. By separating it into translational, rotational, and vibrational parts, we can more accurately understand and analyze motion.

	===~~External Links~~===		==References==
	*https://www.youtube.com/watch?v=5qwW8WI1gkw&feature=youtu.be<br>
	*https://youtu.be/Cobhu3lgeMg<br>
	*https://www.youtube.com/watch?v=craljBk-E5g&feature=youtu.be<br>
	*https://youtu.be/XlFlZHfAZeE<br>
	*https://youtu.be/vL5yTCyRMGk<br>
	*https://en.wikipedia.org/wiki/Kinetic_energy<br>
	*https://en.wikipedia.org/wiki/Moment_of_inertia<br>
	*https://www.khanacademy.org/science/physics/torque-angular-momentum/torque-tutorial/a/rotational-inertia<br>
	*https://youtu.be/vL5yTCyRMGk

	~~==References==~~		*https://openstax.org/details/books/university-physics-volume-1
	~~All problem examples, youtube videos, and images are from the websites referenced below~~:

	*~~http~~://www.~~robjorstad~~.~~com~~/~~Phys161~~/~~161Lab~~/~~161RotationalKinematicsSim.pdf~~		*https://www.khanacademy.org/science/physics/work-and-energy

	*~~http~~://~~p3server~~.pa.~~msu.edu~~/~~coursewiki~~/~~doku.php?id=183_notes:energy_sep~~		*https://en.wikipedia.org/wiki/Kinetic_energy

	*https://~~cnx~~.org/~~contents/1Q9uMg_a@6.4:V7Fr-AEP@3~~/~~103-Relating-Angular-and-Trans~~		*https://en.wikipedia.org/wiki/Moment_of_inertia

	*https://en.~~wikipedia.org~~/~~wiki~~/~~Gaspard-Gustave_de_Coriolis~~		*https://trinket.io/glowscript/

	*https://~~newton~~.~~ph.msstate~~.edu/~~fox~~/~~public_html~~/~~ph2213/examples10-core.pdf~~		*https://ocw.mit.edu/courses/physics/

VPython

Cjahn6 — Wed, 29 Apr 2026 04:05:42 GMT

I killed the python 2.7 / classic vpython stuff (deprecated since 2020), made it all python 3 + glowscript fixed the syntax everywhere: vector() not tuples, hat() not norm(), from vpython import, added the iterative prediction loop section because that's literally the whole point of vpython in 2211 and the old page didn't have it. Also added 3 worked examples: projectile, spring-mass, orbit. all with the momentum form like chabay/sherwood do it.

Show changes

Translational, Rotational and Vibrational Energy

Slakshmisha3 — Wed, 29 Apr 2026 04:04:11 GMT

Rotational Kinetic Energy

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	'''Key Idea:''' Translational energy depends only on how the object moves.		'''Key Idea:''' Translational energy depends only on how the object moves.

	[[File:~~Center_of_mass_diagram.svg\|300px\|center\|thumb\|The~~ center of mass ~~represents the average position~~ of ~~mass in a system~~.]]		[[File:Beam with pivot P, center of mass S and center of percussion C.svg\|Beam_with_pivot_P,_center_of_mass_S_and_center_of_percussion_C]]

	---		---

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	The total energy due to vibrations is the sum of the potential energy associated with interactions causing the vibrations and the kinetic energy of the vibrations.		The total energy due to vibrations is the sum of the potential energy associated with interactions causing the vibrations and the kinetic energy of the vibrations.

	\[		::<math>K_{rot} = \cfrac{1}{2}I\omega^2</math>
	K_{rot} = \~~frac~~{1}{2}I\omega^2
	\]

	* \(I\): moment of inertia
	* \(\omega\): angular velocity

			* <math>I</math>: moment of inertia
			* <math>\omega</math>: angular velocity

	====Moment of Inertia====		====Moment of Inertia====

Newton's Third Law of Motion

Awasil103 — Wed, 29 Apr 2026 04:02:35 GMT

Alexander Wasil, third and final edit, fixed all images erroring when displaying

Show changes

Translational, Rotational and Vibrational Energy

Slakshmisha3 — Wed, 29 Apr 2026 04:01:11 GMT

Translational Kinetic Energy

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	=== Total Kinetic Energy ===		=== Total Kinetic Energy ===

	\[		<math>K_{total} = K_{translational} + K_{rotational} + K_{vibrational}</math>
	K_{total} = K_{translational} + K_{rotational} + K_{vibrational}
	\]

	This equation shows that energy must be considered in multiple forms when objects both move and rotate.		This equation shows that energy must be considered in multiple forms when objects both move and rotate.
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	====Translational Kinetic Energy====		====Translational Kinetic Energy====

	\[		::<math>K_{trans} = \cfrac{1}{2}Mv_{CM}^2</math>
	K_{trans} = \~~frac~~{1}{2}Mv_{CM}^2
	\]

	* \(M\): total mass		* <math>M</math>: total mass
	* \(v_{CM}\): velocity of the center of mass		* <math>v_{CM}</math>: velocity of the center of mass


	The center of mass is calculated as:		The center of mass is calculated as:

	\[		::<math>r_{CM} = \cfrac{\sum m_ir_i}{\sum m_i}</math>
	r_{CM} = \~~frac~~{\sum m_ir_i}{\sum m_i}		::<math>v_{CM} = \cfrac{\sum m_iv_i}{\sum m_i}</math>
	~~\quad\quad~~
	v_{CM} = \~~frac~~{\sum m_iv_i}{\sum m_i}
	\]

	'''Key Idea:''' Translational energy depends only on how the object moves.		'''Key Idea:''' Translational energy depends only on how the object moves.

Newton's Third Law of Motion

Awasil103 — Wed, 29 Apr 2026 03:57:26 GMT

Alexander Wasil, second edit, added image with code i wrote, of two spheres colliding, with force arrows demonstrating newtons third law

← Older revision		Revision as of 23:57, 28 April 2026
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	[https://phet.colorado.edu/sims/collision-lab/collision-lab_en.html PhET Collision Lab]		[https://phet.colorado.edu/sims/collision-lab/collision-lab_en.html PhET Collision Lab]

	~~(custom GlowScript model to prove how this works during a collision~~. ~~the masses were specifically set to be completely different, with one light sphere and one heavy sphere to show that the force is still identical on both~~. )		[[File:Screenshot 2026-04-28 at 11.50.33 PM.png]]

	~~[[File:NewtonsThirdLaw Sim.png\|thumb\|right\|450px\|~~GlowScript model showing colliding spheres with identical force magnitudes of 6 N, proving that action-reaction pairs stay equal regardless of mass.]]		GlowScript model showing colliding spheres with identical force magnitudes of 6 N, proving that action-reaction pairs stay equal regardless of mass.

	==Examples==		==Examples==
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	(b)		(b)
	~~<br>I fixed the misunderstanding here regarding the block interactions. To find the force of block 2 on block 1, you have to look at the force~~

Kinds of Matter

Mshikhalieva3 — Wed, 29 Apr 2026 03:56:45 GMT

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	===Solids===		===Solids===
	~~Solids are a class of matter that retain their~~ shape and size ~~even when not confined by a container and occupy a specific volume~~. ~~They~~ are ~~difficult to deform because~~ they are ~~resistant~~ to ~~changes in shape~~ or ~~volume. The molecules in a solid are generally packed together as much as possible to the extent that the repulsive forces between the molecules allow~~.
	When a solid is heated ~~or when energy is transferred to a solid~~, ~~the~~ molecules gain ~~kinetic~~ energy and ~~eventually overcome the intermolecular forces of attraction that hold them in place~~. ~~If enough kinetic energy is gained, the~~ solid ~~enters~~ a ~~phase change where the~~ solid can ~~become~~ a gas ~~or a liquid~~.		A solid keeps its own shape and size. The molecules are packed tightly and can only vibrate in place - they cannot move around freely. This is why solids are hard to compress or bend.

			When a solid is heated enough, its molecules gain energy and break free. The solid then melts into a liquid. Ice melts at 0 degrees Celsius. A solid can also skip the liquid phase and turn directly into a gas - this is called sublimation. Dry ice (solid CO2) does this at room temperature.

	[[File:solid1.png\|thumb\|Visualization of the molecular arrangement of a solid.]]		[[File:solid1.png\|thumb\|Visualization of the molecular arrangement of a solid.]]
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	===Liquid===		===Liquid===
	Liquid is a phase of matter that can flow, change its shape, and take the shape of its container that it is placed within. Liquids are not easily compressed and maintain a relatively fixed volume. Liquids are made up of molecules that are close together like a solid but lack a defined arrangement as a result of weaker intermolecular forces of attraction. The molecules are able to vibrate, move, and slide past each other in a liquid, which is what allows for changes in shape.

			A liquid flows and takes the shape of its container, but keeps a fixed volume. Molecules in a liquid are close together but can slide past each other, which is why liquids can pour.

			Liquids stay together because of cohesive forces - attractions between molecules of the same substance. When a liquid gains enough energy, it turns into a gas. This is called evaporation. Water boils at 100 degrees Celsius.
	[[File:liquid.png\|thumb\|Molecular arrangement of a liquid.]]		[[File:liquid.png\|thumb\|Molecular arrangement of a liquid.]]



	While particles of gas bounce everywhere and disperse, liquids remain together due to intermolecular forces called cohesive (sticky) forces that act to pull the molecules together. These attractive forces exist between molecules of the same substance and resist separation of a liquid. The liquid can overcome these cohesive forces when the weight (force applied) reaches a certain point.		While particles of gas bounce everywhere and disperse, liquids remain together due to intermolecular forces called cohesive (sticky) forces that act to pull the molecules together. These attractive forces exist between molecules of the same substance and resist separation of a liquid. The liquid can overcome these cohesive forces when the weight (force applied) reaches a certain point.
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	===Gas===		===Gas===
	A gas is a sample of matter that has no definitive shape much like a liquid, but expand to occupy the entire available volume. The molecules in the gaseous state move freely among each other and packed more loosely than the molecules of the same substance in the solid or liquid state. This state of matter is what exists between the liquid and plasma phase, and is usually invisible to the human eye due to the large separation between the molecules. Gases have looser intermolecular bonds than liquids and solids and these bonds exist due to electrostatic interactions between the gas particles where like-charged areas repel and opposite-charged areas attract.

	~~When energy is taken~~ out ~~of a gaseous phase~~, ~~the molecules lose kinetic energy~~ and ~~stop colliding as much~~. ~~The process in which~~ a gas ~~becomes~~ a liquid is called condensation ~~and occurs at the same temperature as the boiling point~~. A gas can directly ~~turn~~ into ~~a solid through a process called deposition. An example of this is when CO2 in air sometimes freezes to directly become~~ a solid, skipping ~~over~~ the liquid phase.		A gas has no fixed shape or volume - it spreads out to fill any container. Gas molecules move freely and are far apart from each other. Examples include oxygen, helium, and water vapor.

			When a gas loses energy, it can turn into a liquid. This is called condensation. A gas can also turn directly into a solid, skipping the liquid phase - this is called deposition.

	===Plasma===		===Plasma===

Translational, Rotational and Vibrational Energy

Slakshmisha3 — Wed, 29 Apr 2026 03:56:24 GMT

Show changes

User:Cjahn6

Cjahn6 — Wed, 29 Apr 2026 03:52:47 GMT

User account Cjahn6 was created

File:Screenshot 2026-04-28 at 11.50.33 PM.png

Awasil103 — Wed, 29 Apr 2026 03:50:56 GMT

Awasil103 uploaded File:Screenshot 2026-04-28 at 11.50.33 PM.png

New page

Kinds of Matter

Mshikhalieva3 — Wed, 29 Apr 2026 03:50:40 GMT

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	==The Main Idea==		==The Main Idea==

	No matter how how big or small the matter, physics can be applied to all objects. States of matter are differentiated or determined by significant changes that occur due to the alteration of an important property such as specific heat capacity, pressure, or temperature. Specific heat capacity is the heat required to raise the temperature of a unit mass by a given amount (usually by one degree). Pressure is a continuous physical force exerted on or against an object and temperature is the degree of heat present in a substance or object. In different states of matter, things only move from one phase to another through physical means and not chemical where the same chemical properties of the substance is the same.

	~~All matter~~ is made ~~of atoms or molecules. To understand the properties~~ of matter ~~around us we look at atomic properties and interactions~~. ~~Atomic interactions~~ can ~~be attributed to the attractive and repulsive forces due to the~~ different ~~parts of an atom which~~ are~~: protons~~, ~~electrons~~, and ~~neutrons~~. ~~Protons are positively charged particles~~, ~~electrons~~ are ~~negative,~~ and ~~neutrons~~ have ~~no charge~~. ~~Protons and neutrons make up~~ a small, dense center called a nucleus. Around the nucleus are electrons~~, whose~~ negative ~~forces are attracted to the positive center~~.		Matter is any substance that has mass and takes up space. Everything around us is made of matter. Matter can exist in different states, also called phases. The four common states are solid, liquid, gas, and plasma. A fifth rare state is the Bose-Einstein condensate.

			Matter moves from one state to another through physical changes, not chemical ones. The substance stays the same - only how its molecules are arranged and how much energy they have changes. These changes are caused by temperature or pressure.

			All matter is made of atoms. Each atom has a small dense center called a nucleus, made of protons (positive charge) and neutrons (no charge). Around the nucleus are electrons (negative charge).

	===Solids===		===Solids===
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	Anything that has mass is made up of matter-- it is essential to almost everything that exists in the universe. The different kinds of matter are important to understanding how physics can be applied to everyday life. It helps connect the misunderstood atomic and subatomic level to something that everyone can understand. More advanced physics will correlate atomic bonds to springs, a juxtaposition that helps explain a complex interaction with a simple explanation.		Anything that has mass is made up of matter-- it is essential to almost everything that exists in the universe. The different kinds of matter are important to understanding how physics can be applied to everyday life. It helps connect the misunderstood atomic and subatomic level to something that everyone can understand. More advanced physics will correlate atomic bonds to springs, a juxtaposition that helps explain a complex interaction with a simple explanation.

	[[File:~~States~~-of-matter.jpg\|~~left~~\|~~thumb\|400px~~\|The change in between matters.]]		[[File:states-of-matter.jpg\|frame\|right\|The change in between matters.]]

	==History==		==History==

File:Screenshot 2026-04-28 at 11.46.13 PM.png

Awasil103 — Wed, 29 Apr 2026 03:46:49 GMT

Awasil103 uploaded File:Screenshot 2026-04-28 at 11.46.13 PM.png file for newtons third law

New page

== Summary ==
file for newtons third law

Real Systems

Sanjan Sen — Wed, 29 Apr 2026 03:40:02 GMT

added a new glowscipt simulation and added step by steps for how to do a real sysem

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 This page describes real systems and how they can be used to model certain aspects of a system's motion.
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 The equation above is the basis for answering work/energy questions using real systems. It is important to remember that when modeling a system as a real system, calculating the work done on the system as described above finds <b>all</b> of the work done on the system- both translational kinetic energy and internal types of energy.
 ===A Computational Model===
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 [[File:Pointparticlesystemtwomass.png]]
-[https://www.glowscript.org/#/user/YorickAndeweg/folder/PhysicsBookFolder/program/twomasssystem Here is a simulation of the system to help you visualize it.]
+[https://www.glowscript.org/#/user/YorickAndeweg/folder/MyPrograms/program/twomasssystem Here is a simulation of the system to help you visualize it.]
 By modeling the system as both a real system and a point particle system (which was done on the point particle systems page), we are able to answer the question. Finding more detailed information about the oscillations, such as their frequency, amplitude, and phase, is much more difficult and requires an entirely real model. A difficult-to-solve system of differential equations would have to be devised, describing the accelerations of the masses in terms of their positions.

File:Force arrows newton.jpg

Awasil103 — Wed, 29 Apr 2026 03:36:55 GMT

Awasil103 uploaded File:Force arrows newton.jpg

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Thermal Energy

Wlu331 — Wed, 29 Apr 2026 03:35:11 GMT

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	Physics Significance: Because it is an absolute scale, Kelvin is the required unit for most calculations in physics (including the Kinetic Molecular Theory and thermal energy equations). It allows physicists to state mathematically that a substance at 200 K has exactly twice the microscopic thermal energy as a substance at 100 K.		Physics Significance: Because it is an absolute scale, Kelvin is the required unit for most calculations in physics (including the Kinetic Molecular Theory and thermal energy equations). It allows physicists to state mathematically that a substance at 200 K has exactly twice the microscopic thermal energy as a substance at 100 K.

			==General Test Tips==

			Writing from the perspective of a Physics 2211 student, here are some things that I found helpful when solving thermal energy problems.

			===Thermal Equilibrium Problems===

			With thermal equilibrium problems, the problem solving process is almost ALWAYS the same.

			First, calculate the initial thermal energy of the system. This includes the total thermal energy of the system, as well as the thermal energy of the substance being added.

			Second, know that the initial thermal energy will always equal the final thermal energy, unless otherwise stated. At thermal equilibrium, the TEMPERATURE is the same, and we should know the masses and specific heat of both substances.

			Third, given all the knowns, we can calculate unknowns using the equation Qtotal = M * C * T, as we know Qtotal and T, and will vary in knowledge between M and C.



	==See also==		==See also==

Kinds of Matter

Mshikhalieva3 — Wed, 29 Apr 2026 03:28:55 GMT

← Older revision		Revision as of 23:28, 28 April 2026
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	Anything that has mass is made up of matter-- it is essential to almost everything that exists in the universe. The different kinds of matter are important to understanding how physics can be applied to everyday life. It helps connect the misunderstood atomic and subatomic level to something that everyone can understand. More advanced physics will correlate atomic bonds to springs, a juxtaposition that helps explain a complex interaction with a simple explanation.		Anything that has mass is made up of matter-- it is essential to almost everything that exists in the universe. The different kinds of matter are important to understanding how physics can be applied to everyday life. It helps connect the misunderstood atomic and subatomic level to something that everyone can understand. More advanced physics will correlate atomic bonds to springs, a juxtaposition that helps explain a complex interaction with a simple explanation.

	[[File:~~states~~-of-matter.jpg\|left\|thumb\|The change in between matters.]]		[[File:States-of-matter.jpg\|left\|thumb\|400px\|The change in between matters.]]

	==History==		==History==

Newton's Third Law of Motion

Awasil103 — Wed, 29 Apr 2026 03:28:41 GMT

Show changes

File:NewtonsThirdLaw Sim.png

Awasil103 — Wed, 29 Apr 2026 03:26:34 GMT

← Older revision		Revision as of 23:26, 28 April 2026
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	<div style="float:right; margin: 10px; border: 1px solid #ccc; padding: ~~10px~~; background: #f9f9f9~~; text-align: center; width: 500px~~;">		<div style="float:right; margin:10px; border:1px solid #ccc; padding:5px; background:#f9f9f9;">
	[[File:NewtonsThirdLaw ~~Sim~~.~~png~~\|~~500px~~]]		[[File:NewtonsThirdLaw.jpg\|450px]]
	<br />		<br />
	<~~p style="font-size: 0.9em; line-height: 1.2em; margin-top: 5px;"~~>		<center><small>GlowScript model: Equal and opposite forces (6 N).</small></center>
	GlowScript model ~~showing colliding spheres with identical force magnitudes of~~ 6 N~~, proving that action-reaction pairs stay equal regardless of mass~~.
	</p>
	</div>		</div>

Kinds of Matter

Mshikhalieva3 — Wed, 29 Apr 2026 03:23:44 GMT

← Older revision		Revision as of 23:23, 28 April 2026
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	Anything that has mass is made up of matter-- it is essential to almost everything that exists in the universe. The different kinds of matter are important to understanding how physics can be applied to everyday life. It helps connect the misunderstood atomic and subatomic level to something that everyone can understand. More advanced physics will correlate atomic bonds to springs, a juxtaposition that helps explain a complex interaction with a simple explanation.		Anything that has mass is made up of matter-- it is essential to almost everything that exists in the universe. The different kinds of matter are important to understanding how physics can be applied to everyday life. It helps connect the misunderstood atomic and subatomic level to something that everyone can understand. More advanced physics will correlate atomic bonds to springs, a juxtaposition that helps explain a complex interaction with a simple explanation.

	[[File:states-of-matter.jpg]]		[[File:states-of-matter.jpg\|left\|thumb\|The change in between matters.]]

	==History==		==History==

File:States-of-matter.jpg

Mshikhalieva3 — Wed, 29 Apr 2026 03:21:49 GMT

Mshikhalieva3 reverted File:States-of-matter.jpg to an old version Reverted to version as of 23:19, 28 April 2026 (EDT)

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File:States-of-matter.jpg

Mshikhalieva3 — Wed, 29 Apr 2026 03:19:57 GMT

Mshikhalieva3 reverted File:States-of-matter.jpg to an old version Reverted to version as of 23:14, 28 April 2026 (EDT)

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File:States-of-matter.jpg

Mshikhalieva3 — Wed, 29 Apr 2026 03:19:42 GMT

Mshikhalieva3 uploaded a new version of File:States-of-matter.jpg

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Kinds of Matter

Mshikhalieva3 — Wed, 29 Apr 2026 03:17:31 GMT

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	===Liquid===		===Liquid===
	Examples: water~~, wine~~, coffee, blood, rubbing alcohol		Examples: water, coffee, blood, rubbing alcohol

	[[File:water.png\|frameless]]		[[File:water.png\|frameless]]
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	Anything that has mass is made up of matter-- it is essential to almost everything that exists in the universe. The different kinds of matter are important to understanding how physics can be applied to everyday life. It helps connect the misunderstood atomic and subatomic level to something that everyone can understand. More advanced physics will correlate atomic bonds to springs, a juxtaposition that helps explain a complex interaction with a simple explanation.		Anything that has mass is made up of matter-- it is essential to almost everything that exists in the universe. The different kinds of matter are important to understanding how physics can be applied to everyday life. It helps connect the misunderstood atomic and subatomic level to something that everyone can understand. More advanced physics will correlate atomic bonds to springs, a juxtaposition that helps explain a complex interaction with a simple explanation.

			[[File:states-of-matter.jpg]]

	==History==		==History==

User:Sanjan Sen

Sanjan Sen — Wed, 29 Apr 2026 03:16:28 GMT

User account Sanjan Sen was created

File:States-of-matter.jpg

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Temperature

Rtleader0 — Wed, 29 Apr 2026 03:09:46 GMT

← Older revision		Revision as of 23:09, 28 April 2026
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	==Main Idea==		==Main Idea==
	[[File:Tempfigure.gif\|300px\|thumb\|right(position)\|]]		[[File:Tempfigure.gif\|300px\|thumb\|right(position)\|]]
	'''EDITED BY ~~Isaac Kim~~ SPRING 26'''		'''EDITED BY ISAAC KIM SPRING 26'''

	Temperature is the measure of the Average Kinetic Energy of the particles in a system. The difference between Temperature, Thermal Energy, and Heat is:		Temperature is the measure of the Average Kinetic Energy of the particles in a system. The difference between Temperature, Thermal Energy, and Heat is:
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	<blockquote>''m represents the mass of the system (can be given in Kg or g depending on the units of C)''</blockquote>		<blockquote>''m represents the mass of the system (can be given in Kg or g depending on the units of C)''</blockquote>
	<blockquote>''C represents the specific heat capcity of the system(Can given in J·kg⁻¹·K⁻¹ or J·g⁻¹·°C⁻¹)''</blockquote>		<blockquote>''C represents the specific heat capcity of the system(Can given in J·kg⁻¹·K⁻¹ or J·g⁻¹·°C⁻¹)''</blockquote>
	<blockquote>''Delta T represents the ~~specific heat capcity~~ of the system(K or °C)''</blockquote>		<blockquote>''Delta T represents the change in temperature of the system (K or °C)''</blockquote>

	====Insulated System====		====Insulated System====

	An insulated system occurs when there is no transfer of heat between the system and the surroundings. Q=0		An insulated system occurs when there is no transfer of heat between the system and the surroundings. Q=0

			====Absolute Zero====
			Absolute zero is the lowest theoretically possible temperature, equal to 0 K, −273.15°C, or −459.67°F. At absolute zero, particles have minimum possible kinetic energy and molecular motion effectively ceases. It is impossible to reach in practice and represents a theoretical lower bound on temperature.

			====Modes of Heat Transfer====
			*'''Conduction''' — Heat transfers through direct molecular contact. Common in solids; metals conduct well while rubber and wood are insulators.

			*'''Convection''' — Heat transfers through bulk fluid movement. Warmer fluid rises, cooler fluid sinks, creating circulation. Example: boiling water.

			*'''Radiation''' — Heat transfers via electromagnetic waves and needs no medium. Example: heat from the Sun reaching Earth.

	====Thermal Expansion====		====Thermal Expansion====
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	::<math>31K: °C = K - 273.15 = 31 - 273.15 = -242.15°C</math>		::<math>31K: °C = K - 273.15 = 31 - 273.15 = -242.15°C</math>

	::<math>-242.~~12°C~~: °F = \left(\frac{9}{5}\right)(°C + 32) = \left(\frac{9}{5}\right)(-~~241~~.15 + 32) = ~~\left(\frac{9}{5}\right)(~~-~~210~~.~~15)~~ = -~~116~~.~~75°F~~</math>		::<math>-242.15°C: °F = \left(\frac{9}{5}\right)(°C) + 32 = \left(\frac{9}{5}\right)(-242.15) + 32 = -435.87 + 32 = -403.87°F</math>

	:''Row 3:''		:''Row 3:''

	::<math>350°C: °F = \left(\frac{9}{5}\right)(°C + 32) = \left(\frac{9}{5}\right)(350 + 32) = ~~\left(\frac{9}{5}\right)(382)~~ = ~~687.2°F~~</math>		::<math>350°C: °F = \left(\frac{9}{5}\right)(°C) + 32 = \left(\frac{9}{5}\right)(350) + 32 = 630 + 32 = 662°F</math>

	::<math>350°C: K = 273.15 + °C = 273.15 + 350 = 623.15K</math>		::<math>350°C: K = 273.15 + °C = 273.15 + 350 = 623.15K</math>
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	\| <math>334.26</math>		\| <math>334.26</math>
	\|-		\|-
	\| <math>-~~116~~.75</math>		\| <math>-403.87</math>
	\| <math>-242.15</math>		\| <math>-242.15</math>
	\| <math>31</math>		\| <math>31</math>
	\|-		\|-
	\| <math>~~687.2~~</math>		\| <math>662</math>
	\| <math>350</math>		\| <math>350</math>
	\| <math>623.15</math>		\| <math>623.15</math>
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	==Connectedness==		==Connectedness==
	~~The idea of~~ Temperature is ~~integral to life. Every morning, millions~~ of ~~people will check the weather for two reasons; to check~~ the ~~Temperature and see if rain is~~ in ~~the forecast~~. We set ~~the Temperature~~ on ~~our~~ ovens ~~daily, select a Temperature on our~~ thermostats, ~~and millions of people will~~ check ~~the~~ weather ~~for two reasons; to check the Temperature~~ and ~~see if rain is~~ in ~~the forecast. Temperature's effects on life are extensive. Thus~~, ~~a thoughtful study of these effects~~ and ~~Temperature is very useful~~ to ~~improve everyday life~~.		Temperature is one of the most universally relevant physical quantities in everyday life. We set temperatures on ovens and thermostats, check weather forecasts, and rely on temperature regulation in medicine, engineering, and food safety. Understanding how temperature relates to thermal energy and heat transfer has broad applications across nearly every scientific and industrial field.

	==History==		==History==
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	In the mid 19th century, Rudolf Clausius showed that Rumford's argument and Caloric Theory can be agreeable if the Caloric Theory included the principle of conservation of energy in place of its original principle of conservation of Heat. By doing so, the Caloric Theory was able to be evolved into modern Thermodynamics where Heat is described as the transfer of Thermal Energy, which is equivalent to the kinetic energy of the particles of a substance.		In the mid 19th century, Rudolf Clausius showed that Rumford's argument and Caloric Theory can be agreeable if the Caloric Theory included the principle of conservation of energy in place of its original principle of conservation of Heat. By doing so, the Caloric Theory was able to be evolved into modern Thermodynamics where Heat is described as the transfer of Thermal Energy, which is equivalent to the kinetic energy of the particles of a substance.

			Daniel Gabriel Fahrenheit developed his temperature scale in 1724, Anders Celsius proposed his scale in 1742, and William Thomson (Lord Kelvin) introduced the absolute temperature scale in 1848, anchoring it at absolute zero.

	==See also==		==See also==

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Thermal Energy

Wlu331 — Wed, 29 Apr 2026 02:58:43 GMT

History

← Older revision		Revision as of 22:58, 28 April 2026
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	Thermal Energy was discovered by a man named James Joule in the 1840's. Careful experiments showed that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. Joule carried out one of the most famous experiments, demonstrating this fact. Joule hung some weights from pulleys, so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4,200 Joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: Thermal Energy, which manifests itself as an increase or decrease in temperature.		Thermal Energy was discovered by a man named James Joule in the 1840's. Careful experiments showed that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. Joule carried out one of the most famous experiments, demonstrating this fact. Joule hung some weights from pulleys, so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4,200 Joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: Thermal Energy, which manifests itself as an increase or decrease in temperature.

	The Fahrenheit Scale (1724)		===The Fahrenheit Scale (1724)===
	Developed by the physicist Daniel Gabriel Fahrenheit, this was the first standardized temperature scale to gain widespread use, largely because Fahrenheit also invented the first reliable mercury-in-glass thermometer.		Developed by the physicist Daniel Gabriel Fahrenheit, this was the first standardized temperature scale to gain widespread use, largely because Fahrenheit also invented the first reliable mercury-in-glass thermometer.

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	The Adjustment: The scale was later slightly recalibrated so that the boiling point of water would be exactly 212°F, creating exactly 180 degrees of separation between the freezing and boiling points of water at sea level. This recalibration shifted normal human body temperature to roughly 98.6°F.		The Adjustment: The scale was later slightly recalibrated so that the boiling point of water would be exactly 212°F, creating exactly 180 degrees of separation between the freezing and boiling points of water at sea level. This recalibration shifted normal human body temperature to roughly 98.6°F.

	The Celsius Scale (1742)		===The Celsius Scale (1742)===
	Created by the Swedish astronomer Anders Celsius, this scale aimed to simplify thermometry by strictly anchoring it to the phase changes of water and utilizing a base-100 system.		Created by the Swedish astronomer Anders Celsius, this scale aimed to simplify thermometry by strictly anchoring it to the phase changes of water and utilizing a base-100 system.

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	The Inversion: Shortly after Celsius's death in 1744, the Swedish botanist Carl Linnaeus (along with other scientists) inverted the scale to the modern format we use today, where 0°C is freezing and 100°C is boiling. For a long time, it was simply called the "centigrade" scale (meaning 100 steps) until it was officially named after Celsius in 1948.		The Inversion: Shortly after Celsius's death in 1744, the Swedish botanist Carl Linnaeus (along with other scientists) inverted the scale to the modern format we use today, where 0°C is freezing and 100°C is boiling. For a long time, it was simply called the "centigrade" scale (meaning 100 steps) until it was officially named after Celsius in 1948.

	The Kelvin Scale (1848)		===The Kelvin Scale (1848)===
	While Fahrenheit and Celsius are based on arbitrary observable phenomena (like freezing water or brine), the Kelvin scale is rooted in fundamental thermodynamics. It was proposed by the Scottish physicist William Thomson, 1st Baron Kelvin.		While Fahrenheit and Celsius are based on arbitrary observable phenomena (like freezing water or brine), the Kelvin scale is rooted in fundamental thermodynamics. It was proposed by the Scottish physicist William Thomson, 1st Baron Kelvin.

Temperature

Rtleader0 — Wed, 29 Apr 2026 02:53:38 GMT

← Older revision		Revision as of 22:53, 28 April 2026
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	==Main Idea==		==Main Idea==
	[[File:Tempfigure.gif\|300px\|thumb\|right(position)\|]]		[[File:Tempfigure.gif\|300px\|thumb\|right(position)\|]]
	'''EDITED BY ~~MASON FOSDICK FALL25~~'''		'''EDITED BY Isaac Kim SPRING 26'''

	Temperature is the measure of the Average Kinetic Energy of the particles in a system. The difference between Temperature, Thermal Energy, and Heat is:		Temperature is the measure of the Average Kinetic Energy of the particles in a system. The difference between Temperature, Thermal Energy, and Heat is:

Thermal Energy

Wlu331 — Wed, 29 Apr 2026 02:52:18 GMT

History

← Older revision		Revision as of 22:52, 28 April 2026
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	'''Claimed by William Lu (Spring 2026)'''		'''Claimed by William Lu (Spring 2026)'''

	==~~Main Idea~~==		==Overview==
	All objects are made up of atoms and molecules-- so many that it would take longer than the ~~Universe~~'s estimated lifetime to count. ~~The~~ constant and random motion of an object's atoms ~~or molecules~~ is what determines its Thermal Energy. Thermal Energy is a component of internal energy, but is unrelated to the vibrational and rotational energy of a solid's atoms. Instead, Thermal Energy occurs from atoms' translational motion.		All objects are made up of atoms and, on a larger scale, molecules-- so many that it would take longer than the universe's estimated lifetime to count. At an atomic scale, all particles hold an internal kinetic energy, such that no subatomic particle is ever fully still. This constant and random motion of an object's atoms is what determines its Thermal Energy. Thermal Energy is a component of internal energy, but is unrelated to the vibrational and rotational energy of a solid's atoms. Instead, Thermal Energy occurs from atoms' translational motion as a result of their internal kinetic energy.

	When we say "change of thermal energy," we mean that it is the part of the internal energy that is associated with a [[Thermal Energy#Temperature\| Temperature]] change. Thermal Energy is quantified using temperature. This quantification describes the approximate average ~~Thermal~~ Kinetic Energy present in all of the atoms or molecules in the object/sample/system. In the real world, it is often impossible to accurately state how much of an object's internal energy is Thermal. However, if the Heat Capacity and mass of am object is known, we can measure its temperature using a thermometer and calculate its Thermal Energy.		When we say "change of thermal energy," we mean that it is the part of the internal energy that is associated with a [[Thermal Energy#Temperature\| Temperature]] change. Thermal Energy is quantified using temperature. This quantification describes the approximate average Kinetic Energy present across all of the atoms or molecules in the object/sample/system. In the real world, it is often impossible to accurately state how much of an object's internal energy is Thermal. However, if the Heat Capacity and mass of an object are known, we can measure its temperature using a thermometer and calculate its Thermal Energy.

	===A Mathematical Model===		===A Mathematical Model===
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	==History==		==History==
	Thermal Energy was discovered by a man named James Joule in the 1840's. Careful experiments showed that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. Joule carried out one of the most famous experiments, demonstrating this fact. Joule hung some weights from pulleys, so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4,200 Joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: Thermal Energy, which manifests itself as an increase or decrease in temperature.		Thermal Energy was discovered by a man named James Joule in the 1840's. Careful experiments showed that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. Joule carried out one of the most famous experiments, demonstrating this fact. Joule hung some weights from pulleys, so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4,200 Joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: Thermal Energy, which manifests itself as an increase or decrease in temperature.

			The Fahrenheit Scale (1724)
			Developed by the physicist Daniel Gabriel Fahrenheit, this was the first standardized temperature scale to gain widespread use, largely because Fahrenheit also invented the first reliable mercury-in-glass thermometer.

			The Original Reference Points: Fahrenheit initially based his scale on three points. He set 0°F at the freezing point of a brine mixture (water, ice, and ammonium chloride), which was the lowest temperature he could artificially reproduce in a lab. He set 32°F as the freezing point of pure water, and 96°F as the approximate human body temperature.

			The Adjustment: The scale was later slightly recalibrated so that the boiling point of water would be exactly 212°F, creating exactly 180 degrees of separation between the freezing and boiling points of water at sea level. This recalibration shifted normal human body temperature to roughly 98.6°F.

			The Celsius Scale (1742)
			Created by the Swedish astronomer Anders Celsius, this scale aimed to simplify thermometry by strictly anchoring it to the phase changes of water and utilizing a base-100 system.

			The Original "Reversed" Scale: In Celsius's original 1742 publication, he actually set the boiling point of water at 0°C and the freezing point at 100°C to avoid negative numbers when measuring cold winter temperatures in Sweden.

			The Inversion: Shortly after Celsius's death in 1744, the Swedish botanist Carl Linnaeus (along with other scientists) inverted the scale to the modern format we use today, where 0°C is freezing and 100°C is boiling. For a long time, it was simply called the "centigrade" scale (meaning 100 steps) until it was officially named after Celsius in 1948.

			The Kelvin Scale (1848)
			While Fahrenheit and Celsius are based on arbitrary observable phenomena (like freezing water or brine), the Kelvin scale is rooted in fundamental thermodynamics. It was proposed by the Scottish physicist William Thomson, 1st Baron Kelvin.

			The Discovery of Absolute Zero: By the mid-1800s, scientists studying gases noticed a linear relationship between volume and temperature. Extrapolating this line backward suggested that at approximately -273.15°C, the volume (and pressure) of an ideal gas would drop to zero. Kelvin recognized this as "absolute zero"—the theoretical point where all microscopic thermal kinetic energy ceases.

			The Scale: Kelvin proposed a new scale that started at absolute zero but maintained the exact same increment size as the Celsius scale. Therefore, 0 K is absolute zero, water freezes at 273.15 K, and water boils at 373.15 K.

			Physics Significance: Because it is an absolute scale, Kelvin is the required unit for most calculations in physics (including the Kinetic Molecular Theory and thermal energy equations). It allows physicists to state mathematically that a substance at 200 K has exactly twice the microscopic thermal energy as a substance at 100 K.

	==See also==		==See also==

Magnetic Field of a Loop

Joogps — Wed, 29 Apr 2026 02:47:45 GMT

← Older revision		Revision as of 22:47, 28 April 2026
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	==Electromagnetic Induction==		==Electromagnetic Induction==



	[[File:Induction_experiment.png\|thumb\|300px\|Faraday's electromagnetic induction experiment. Source: Wikimedia Commons, public domain.]]		[[File:Induction_experiment.png\|thumb\|300px\|Faraday's electromagnetic induction experiment. Source: Wikimedia Commons, public domain.]]
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	The negative sign reflects '''Lenz's Law''': the induced current flows in a direction that opposes the change in flux that caused it. For example, if the magnetic flux through a loop is increasing, the induced current will flow in the direction that creates a magnetic field opposing that increase — effectively trying to keep the flux constant. This is consistent with the right hand rule discussed above. If you know the direction of the induced magnetic field (opposing the change), curling the fingers of your right hand in the direction of the induced current will confirm its flow direction around the loop.		The negative sign reflects '''Lenz's Law''': the induced current flows in a direction that opposes the change in flux that caused it. For example, if the magnetic flux through a loop is increasing, the induced current will flow in the direction that creates a magnetic field opposing that increase — effectively trying to keep the flux constant. This is consistent with the right hand rule discussed above. If you know the direction of the induced magnetic field (opposing the change), curling the fingers of your right hand in the direction of the induced current will confirm its flow direction around the loop.

			[[File:Itaipu-Wasserkraftwerk_Generator.JPG\|left\|thumb\|300px\|One of the 700 MW generators inside the Itaipu hydroelectric dam. Source: Wikimedia Commons, CC BY-SA 3.0.]]

	This principle is exactly how electric generators work. In a simple generator, a loop of wire (or a coil with <math>N</math> turns) is rotated inside a uniform external magnetic field. As the loop spins, the angle <math>\theta</math> between the field and the loop's normal vector changes continuously, causing the flux <math>\Phi_B = B A \cos\theta</math> to vary sinusoidally with time. By Faraday's Law, this produces an alternating emf. For a coil of <math>N</math> turns rotating at angular velocity <math>\omega</math>, the induced emf is:		This principle is exactly how electric generators work. In a simple generator, a loop of wire (or a coil with <math>N</math> turns) is rotated inside a uniform external magnetic field. As the loop spins, the angle <math>\theta</math> between the field and the loop's normal vector changes continuously, causing the flux <math>\Phi_B = B A \cos\theta</math> to vary sinusoidally with time. By Faraday's Law, this produces an alternating emf. For a coil of <math>N</math> turns rotating at angular velocity <math>\omega</math>, the induced emf is:

	::<math>\mathcal{E} = N B A \omega \sin(\omega t)</math>		::<math>\mathcal{E} = N B A \omega \sin(\omega t)</math>


	~~[[File:Itaipu-Wasserkraftwerk_Generator.JPG\|left\|thumb\|300px\|One of the 700 MW generators inside the Itaipu hydroelectric dam. Source: Wikimedia Commons, CC BY-SA 3.0.]]~~

	This is the origin of alternating current (AC) electricity. The same loop geometry analyzed in the earlier sections of this page directly determines how much voltage a generator produces. Increasing the number of loops <math>N</math>, the area of each loop, the strength of the external magnetic field, or the rotation speed all increase the output. Power plants, whether they burn fuel, use nuclear reactions, or harness wind and water, all ultimately spin a coil inside a magnetic field to generate electricity using this principle.		This is the origin of alternating current (AC) electricity. The same loop geometry analyzed in the earlier sections of this page directly determines how much voltage a generator produces. Increasing the number of loops <math>N</math>, the area of each loop, the strength of the external magnetic field, or the rotation speed all increase the output. Power plants, whether they burn fuel, use nuclear reactions, or harness wind and water, all ultimately spin a coil inside a magnetic field to generate electricity using this principle.

	One of the most striking real-world examples of electromagnetic induction at scale is the Itaipu Dam, a binational hydroelectric plant on the Paraná River between Brazil and Paraguay. The dam's 20 generating units each produce 700 MW by channeling river water through massive turbines that spin generator coils inside strong magnetic fields, directly applying the mathematical relationship described above. With a total installed capacity of 14 GW, Itaipu is one of the largest hydroelectric plants in the world and demonstrates how the physics of a single current-carrying loop scales up to power entire countries.		One of the most striking real-world examples of electromagnetic induction at scale is the Itaipu Dam, a binational hydroelectric plant on the Paraná River between Brazil and Paraguay. The dam's 20 generating units each produce 700 MW by channeling river water through massive turbines that spin generator coils inside strong magnetic fields, directly applying the mathematical relationship described above. With a total installed capacity of 14 GW, Itaipu is one of the largest hydroelectric plants in the world and demonstrates how the physics of a single current-carrying loop scales up to power entire countries.

			For more on how inductors use these principles, see [[Inductors]].

			<br clear="all">

	==Connectedness==		==Connectedness==

	Magnetic fields from electric loops are observed often in science and industrial applications. For example, a solenoid is often modeled as a bunch of loops contributing to a collective magnetic field. It is important to be able to model the field, since many scientific applications of magnetism involve circular loops. The calculations can be compared to experiments done in the lab.		Magnetic fields from electric loops are observed often in science and industrial applications. For example, a solenoid is often modeled as a bunch of loops contributing to a collective magnetic field. It is important to be able to model the field, since many scientific applications of magnetism involve circular loops. The calculations can be compared to experiments done in the lab.

User:Rtleader0

Rtleader0 — Wed, 29 Apr 2026 02:46:08 GMT

User account Rtleader0 was created

Magnetic Field of a Loop

Joogps — Wed, 29 Apr 2026 02:45:06 GMT

← Older revision		Revision as of 22:45, 28 April 2026
(One intermediate revision by the same user not shown)
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	==Electromagnetic Induction==		==Electromagnetic Induction==

			[[File:Induction_experiment.png\|thumb\|300px\|Faraday's electromagnetic induction experiment. Source: Wikimedia Commons, public domain.]]

	The previous sections describe how a current flowing through a loop produces a magnetic field. The reverse process is equally important: a changing magnetic field through a loop can produce a current. This phenomenon, known as electromagnetic induction, was discovered by Michael Faraday in 1831 and is the basis for nearly all modern electricity generation.		The previous sections describe how a current flowing through a loop produces a magnetic field. The reverse process is equally important: a changing magnetic field through a loop can produce a current. This phenomenon, known as electromagnetic induction, was discovered by Michael Faraday in 1831 and is the basis for nearly all modern electricity generation.

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	::<math>\mathcal{E} = N B A \omega \sin(\omega t)</math>		::<math>\mathcal{E} = N B A \omega \sin(\omega t)</math>


			[[File:Itaipu-Wasserkraftwerk_Generator.JPG\|left\|thumb\|300px\|One of the 700 MW generators inside the Itaipu hydroelectric dam. Source: Wikimedia Commons, CC BY-SA 3.0.]]

	This is the origin of alternating current (AC) electricity. The same loop geometry analyzed in the earlier sections of this page directly determines how much voltage a generator produces. Increasing the number of loops <math>N</math>, the area of each loop, the strength of the external magnetic field, or the rotation speed all increase the output. Power plants, whether they burn fuel, use nuclear reactions, or harness wind and water, all ultimately spin a coil inside a magnetic field to generate electricity using this principle.		This is the origin of alternating current (AC) electricity. The same loop geometry analyzed in the earlier sections of this page directly determines how much voltage a generator produces. Increasing the number of loops <math>N</math>, the area of each loop, the strength of the external magnetic field, or the rotation speed all increase the output. Power plants, whether they burn fuel, use nuclear reactions, or harness wind and water, all ultimately spin a coil inside a magnetic field to generate electricity using this principle.

			One of the most striking real-world examples of electromagnetic induction at scale is the Itaipu Dam, a binational hydroelectric plant on the Paraná River between Brazil and Paraguay. The dam's 20 generating units each produce 700 MW by channeling river water through massive turbines that spin generator coils inside strong magnetic fields, directly applying the mathematical relationship described above. With a total installed capacity of 14 GW, Itaipu is one of the largest hydroelectric plants in the world and demonstrates how the physics of a single current-carrying loop scales up to power entire countries.

	==Connectedness==		==Connectedness==
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	*[[Biot-Savart Law for Currents]]<br>		*[[Biot-Savart Law for Currents]]<br>
	*[[Current]]<br>		*[[Current]]<br>
			*[[Inductors]]<br>

	==References==		==References==

Translational, Rotational and Vibrational Energy

Slakshmisha3 — Wed, 29 Apr 2026 02:41:17 GMT

← Older revision		Revision as of 22:41, 28 April 2026
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	~~GABRIEL ALMEIDA~~ SPRING ~~2022~~		SHREYA LAKSHMISHA SPRING 2026

	==Main Idea==		==Main Idea==