Total Angular Momentum - Revision history

Ayoo49 at 03:22, 3 December 2025

2025-12-03T03:22:51Z

← Older revision		Revision as of 23:22, 2 December 2025
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	~~Daniel O'Connor~~ Fall ~~2023~~		Anthony Yoo Fall 2026

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

Ayoo49: I added a completely new section explaining the difference between translational and rotational angular momentum, including clear formulas, definitions, and how they combine to form total angular momentum. This section helps readers understand when each type applies and why real systems often contain both contributions.

2025-12-03T03:22:36Z

I added a completely new section explaining the difference between translational and rotational angular momentum, including clear formulas, definitions, and how they combine to form total angular momentum. This section helps readers understand when each type applies and why real systems often contain both contributions.

← Older revision		Revision as of 23:22, 2 December 2025
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	This screenshot shows the code in action but you can check it out with this link: '''https://trinket.io/glowscript/49129c12fd'''		This screenshot shows the code in action but you can check it out with this link: '''https://trinket.io/glowscript/49129c12fd'''

			==Rotational vs. Translational Angular Momentum==

			Angular momentum can arise from two physically different types of motion: the motion of a system's center of mass (translational), and the spinning or rotation of the system around its own internal axis (rotational). Many real physical systems contain both types at the same time. This section expands on how these two contributions are defined and how they combine to form the total angular momentum.

			===Translational Angular Momentum===

			Translational angular momentum comes from the motion of the system’s center of mass relative to a chosen origin. Even if an object is not spinning, it still has angular momentum if its center of mass moves along a straight or curved path that does not pass through the origin.

			The translational contribution is given by:

			:<math> \vec{L}{trans} = \vec{r}{cm} \times \vec{p}_{cm} </math>

			where:

			<math>\vec{r}_{cm}</math> is the position of the center of mass relative to the chosen origin

			<math>\vec{p}{cm} = m\vec{v}{cm}</math> is the linear momentum of the entire system

			Key idea: Translational angular momentum depends entirely on the center of mass motion and not on any internal rotation.

			===Rotational Angular Momentum (“Spin”)===

			Rotational or spin angular momentum comes from an object rotating about an internal axis that passes through its center of mass. This type of angular momentum exists even if the object is not moving through space (i.e., the center of mass is stationary).

			It is given by:

			:<math> \vec{L}_{rot} = I\vec{\omega} </math>

			where:

			<math>I</math> is the rotational inertia about the axis through the center of mass

			<math>\vec{\omega}</math> is the angular velocity vector

			Key idea: Rotational angular momentum describes the internal spinning motion of the object.

			===Total Angular Momentum===

			For extended bodies or multi-part systems, the total angular momentum is the vector sum of the translational and rotational contributions:

			:<math> \vec{L}{total} = \vec{L}{trans} + \vec{L}_{rot} </math>

			This decomposition is extremely useful in physics because:

			Some problems only involve <math>\vec{L}_{trans}</math> (e.g., a thrown ball that is not spinning).

			Others only involve <math>\vec{L}_{rot}</math> (e.g., a spinning disk fixed at its center).

			Most real systems involve both (e.g., planets rotating while orbiting, wheels rolling without slipping, gymnasts flipping).

			Understanding which type of angular momentum is present helps determine what torques act on the system and whether the total angular momentum is conserved.

	==Examples==		==Examples==

DanOConnor: /* Connectedness */

2023-12-04T02:07:13Z

Connectedness

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 The link to the code:
 https://www.glowscript.org/#/user/danielisme18/folder/MyPrograms/program/angularMomentump1
 ==History==

DanOConnor: /* Computational Model for this problem */

2023-12-04T02:02:24Z