Relativistic Momentum - Revision history

YorickAndeweg: /* Difficult */

2019-08-03T19:11:38Z

Difficult

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	<math> \vec{p} = 3.203 * 1.7 * 10^{-27} * (.95 * 3 * 10^8) = 1.55 * 10^{-18} </math> kg*m/s		<math> \vec{p} = 3.203 * 1.7 * 10^{-27} * (.95 * 3 * 10^8) = 1.55 * 10^{-18} </math> kg*m/s

	Now let us find the momentum at the end of the impulse using the impulse-momentum theorem ~~(see [[impulse and momentum~~]]).		Now let us find the momentum at the end of the impulse using the [[Impulse and Momentum\|impulse-momentum theorem]].

	<math> \vec{p}_f = \vec{p}_i + \vec{J} </math>		<math> \vec{p}_f = \vec{p}_i + \vec{J} </math>

YorickAndeweg: /* The Main Idea */

2019-08-03T19:11:10Z

The Main Idea

← Older revision		Revision as of 15:11, 3 August 2019
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	==The Main Idea==		==The Main Idea==

	The [[Linear Momentum]] of an object is traditionally defined as <math>\vec{p} = m \vec{v}</math>. Momentum is a useful quantity because many other concepts relate to it. For example, forces cause the momentum of a system to change according to [[Newton's Second Law: the Momentum Principle]], and in certain situations, [[Conservation of Momentum]]\|the momentum of a system is conserved]]. However, for systems containing objects moving at speeds comparable to the speed of light, both Newton's second law and conservation of momentum appear to be violated. As it turns out, if the definition of the momentum of a particle is adjusted to accommodate high-speed objects, these relations hold true after all. The adjusted definition of momentum is called the relativistic definition and defines momentum as follows:		The [[Linear Momentum]] of an object is traditionally defined as <math>\vec{p} = m \vec{v}</math>. Momentum is a useful quantity because many other concepts relate to it. For example, forces cause the momentum of a system to change according to [[Newton's Second Law: the Momentum Principle]], and in certain situations, [[Conservation of Momentum\|the momentum of a system is conserved]]. However, for systems containing objects moving at speeds comparable to the speed of light, both Newton's second law and conservation of momentum appear to be violated. As it turns out, if the definition of the momentum of a particle is adjusted to accommodate high-speed objects, these relations hold true after all. The adjusted definition of momentum is called the relativistic definition and defines momentum as follows:

	<math> \vec{p} = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} * m \vec{v} </math>		<math> \vec{p} = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} * m \vec{v} </math>

YorickAndeweg: /* The Main Idea */

2019-08-03T19:10:48Z

The Main Idea

← Older revision		Revision as of 15:10, 3 August 2019
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	==The Main Idea==		==The Main Idea==

	The [[Linear Momentum]] of an object is traditionally defined as <math>\vec{p} = m \vec{v}</math>. Momentum is a useful quantity because many other concepts relate to it. For example, forces cause the momentum of a system to change according to [[Newton's Second Law: the Momentum Principle]], and in certain situations, the momentum of a system is conserved ~~(see [[Conservation of Momentum~~]]). However, for systems containing objects moving at speeds comparable to the speed of light, both Newton's second law and conservation of momentum appear to be violated. As it turns out, if the definition of the momentum of a particle is adjusted to accommodate high-speed objects, these relations hold true after all. The adjusted definition of momentum is called the relativistic definition and defines momentum as follows:		The [[Linear Momentum]] of an object is traditionally defined as <math>\vec{p} = m \vec{v}</math>. Momentum is a useful quantity because many other concepts relate to it. For example, forces cause the momentum of a system to change according to [[Newton's Second Law: the Momentum Principle]], and in certain situations, [[Conservation of Momentum]]\|the momentum of a system is conserved]]. However, for systems containing objects moving at speeds comparable to the speed of light, both Newton's second law and conservation of momentum appear to be violated. As it turns out, if the definition of the momentum of a particle is adjusted to accommodate high-speed objects, these relations hold true after all. The adjusted definition of momentum is called the relativistic definition and defines momentum as follows:

	<math> \vec{p} = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} * m \vec{v} </math>		<math> \vec{p} = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} * m \vec{v} </math>

YorickAndeweg: /* The Main Idea */

2019-08-03T19:08:51Z

The Main Idea

← Older revision		Revision as of 15:08, 3 August 2019
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	==The Main Idea==		==The Main Idea==

	The [[Linear ~~momentum~~]] of an object is traditionally defined as <math>\vec{p} = m \vec{v}</math>. Momentum is a useful quantity because many other concepts relate to it. For example, forces cause the momentum of a system to change according to [[Newton's Second Law: the Momentum Principle]], and in certain situations, the momentum of a system is conserved (see [[Conservation of Momentum]]). However, for systems containing objects moving at speeds comparable to the speed of light, both Newton's second law and conservation of momentum appear to be violated. As it turns out, if the definition of the momentum of a particle is adjusted to accommodate high-speed objects, these relations hold true after all. The adjusted definition of momentum is called the relativistic definition and defines momentum as follows:		The [[Linear Momentum]] of an object is traditionally defined as <math>\vec{p} = m \vec{v}</math>. Momentum is a useful quantity because many other concepts relate to it. For example, forces cause the momentum of a system to change according to [[Newton's Second Law: the Momentum Principle]], and in certain situations, the momentum of a system is conserved (see [[Conservation of Momentum]]). However, for systems containing objects moving at speeds comparable to the speed of light, both Newton's second law and conservation of momentum appear to be violated. As it turns out, if the definition of the momentum of a particle is adjusted to accommodate high-speed objects, these relations hold true after all. The adjusted definition of momentum is called the relativistic definition and defines momentum as follows:

	<math> \vec{p} = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} * m \vec{v} </math>		<math> \vec{p} = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} * m \vec{v} </math>

YorickAndeweg: /* Examples */

2019-07-07T18:27:42Z

Examples

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	Suppose that a proton (mass = <math> 1.7 * 10^{-27} </math> kg) is moving with a speed of <math> .97c </math> <br>		Suppose that a proton (mass = <math> 1.7 * 10^{-27} </math> kg) is moving with a speed of <math> .97c </math> <br>
	<br> What is the magnitude of the momentum of the proton?		<br> What is the magnitude of the momentum of the proton?

			Solution:

	:<math> \frac{v}{c} = \frac{.97c}{c}</math> <math> = .97 </math>		:<math> \frac{v}{c} = \frac{.97c}{c}</math> <math> = .97 </math>
	:<math> \gamma = \frac{1}{\sqrt{1-(.97)^2}} = 4.1135 </math>		:<math> \gamma = \frac{1}{\sqrt{1-(.97)^2}} = 4.1135 </math>
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	Suppose that a proton (mass = <math> 1.7 * 10^{-27} </math> kg) is moving with a velocity <math> <1 * 10^7 , 2 * 10^7 , 3 * 10^7> </math> m/s. <br>		Suppose that a proton (mass = <math> 1.7 * 10^{-27} </math> kg) is moving with a velocity <math> <1 * 10^7 , 2 * 10^7 , 3 * 10^7> </math> m/s. <br>
	<br> What is the momentum of the proton?		<br> What is the momentum of the proton?

			Solution:

	:<math> \left\vert \overrightarrow{v} \right\vert = \sqrt{(110^7)^2 + (210^7)^2 +(310^7)^2} </math> m/s <math> = 3.7 10^7 </math> m/s.		:<math> \left\vert \overrightarrow{v} \right\vert = \sqrt{(110^7)^2 + (210^7)^2 +(310^7)^2} </math> m/s <math> = 3.7 10^7 </math> m/s.
	:<math> \frac{\left\vert \overrightarrow{v} \right\vert}{c} = \frac{3.7 * 10^7 m/s}{3 * 10^8 m/s}</math> <math> = .12 </math>		:<math> \frac{\left\vert \overrightarrow{v} \right\vert}{c} = \frac{3.7 * 10^7 m/s}{3 * 10^8 m/s}</math> <math> = .12 </math>
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	Suppose that a proton (mass = <math> 1.7 * 10^{-27} </math> kg) is moving at a speed of <math>.95c</math>. A force of magnitude <math>2 * 10^{-17}</math>N acts on it for .5s in the direction of the proton's velocity, causing it to speed up. What is its new speed at the end of the .5s time interval? Use <math>3*10^8</math> for <math>c</math>.		Suppose that a proton (mass = <math> 1.7 * 10^{-27} </math> kg) is moving at a speed of <math>.95c</math>. A force of magnitude <math>2 * 10^{-17}</math>N acts on it for .5s in the direction of the proton's velocity, causing it to speed up. What is its new speed at the end of the .5s time interval? Use <math>3*10^8</math> for <math>c</math>.

			Solution:

	Let us first find the initial momentum of the particle:		Let us first find the initial momentum of the particle:

YorickAndeweg: /* References */

2019-06-07T02:26:27Z

References

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	==References==		==References==
	*https://opentextbc.ca/physicstestbook2/chapter/relativistic-momentum/		*https://opentextbc.ca/physicstestbook2/chapter/relativistic-momentum/

			[[Category:Momentum]]

YorickAndeweg: /* Connectedness */

2019-06-04T18:38:45Z

Connectedness

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	==Connectedness==		==Connectedness==

	Relativistic momentum has applications in quantum physics, particle physics, and astrophysics. In these branches of physics, particles routinely travel at relativistic speeds, and often, their momenta are directly measurable by the particles' interactions with matter. In industry, relativistic momentum is mostly used by ~~the~~ space flight ~~industry~~.		Relativistic momentum has applications in quantum physics, particle physics, and astrophysics. In these branches of physics, particles routinely travel at relativistic speeds, and often, their momenta are directly measurable by the particles' interactions with matter. In industry, relativistic momentum is mostly used by space flight institutions.

	==History==		==History==

YorickAndeweg: /* History */

2019-05-29T16:51:10Z

History

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	==History==		==History==

	In 1905, [[Albert Einstein]] ~~released~~ his Special Theory of Relativity ~~to the public~~. This theory set the "speed limit" for the universe at the speed of light. ~~When objects, came closer to~~ the speed of light, ~~many entities are drastically changed (one being momentum). This changed~~ the ~~direction~~ of physics ~~immensely~~. After this discovery, physicists were better able to ~~predict and calculate momentum on~~ the ~~microscopic scale~~ of fast-moving particles.		In 1905, [[Albert Einstein]] published his Special Theory of Relativity. This theory set the "speed limit" for the universe at the speed of light and redefined many properties such as momentum and energy for fast-moving objects. As particles' speeds approach the speed of light, the laws of physics change even for concepts as fundamental as space and time. After this discovery, physicists were better able to understand the motion of fast-moving particles. Einstein published the more comprehensive General Theory of Relativity in 1915, which allowed differently accelerating frames of reference to be reconciled. Some aspects of relativity have since been used in a variety of technologies, including GPS.

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

YorickAndeweg: /* See also */

2019-05-29T16:39:05Z

YorickAndeweg: /* See also */

2019-05-29T16:37:10Z

← Older revision		Revision as of 12:39, 29 May 2019
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	== See also ==		== See also ==

	[[Linear Momentum]]		*[[Linear Momentum]]
	[[Newton's Second Law: the Momentum Principle]]		*[[Newton's Second Law: the Momentum Principle]]
	[[Impulse and Momentum]]		*[[Impulse and Momentum]]
	[[Mass]]		*[[Mass]]
	[[Vectors]]		*[[Vectors]]

	===~~Further reading~~===		===External Links===

			*http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/relmom.html

	==References==		==References==
	*https://opentextbc.ca/physicstestbook2/chapter/relativistic-momentum/		*https://opentextbc.ca/physicstestbook2/chapter/relativistic-momentum/

← Older revision		Revision as of 12:37, 29 May 2019
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	== See also ==		== See also ==

	~~Links to different uses of momentum~~		[[Linear Momentum]]
			[[Newton's Second Law: the Momentum Principle]]
			[[Impulse and Momentum]]
			[[Mass]]
			[[Vectors]]

	===Further reading===		===Further reading===

	*[http://www.physicsbook.gatech.edu/Momentum_Principle Momentum Principle]
	*[http://www.physicsbook.gatech.edu/Impulse_Momentum Impulse Momentum]
	*[http://www.physicsbook.gatech.edu/Momentum_with_respect_to_external_Forces Momentum with Respect to External Forces]
	*[http://www.physicsbook.gatech.edu/Iterative_Prediction Iterative Prediction and Position Update]

	==References==		==References==
	*https://opentextbc.ca/physicstestbook2/chapter/relativistic-momentum/		*https://opentextbc.ca/physicstestbook2/chapter/relativistic-momentum/