Does more angular monentum mean faster spin?

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Discussion Overview

The discussion centers around the relationship between angular momentum and angular velocity, particularly whether a higher angular momentum necessarily indicates a faster spin. Participants explore this concept through examples involving a top and the Earth, considering factors such as moment of inertia.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions if the Earth, with greater angular momentum than a top, must be spinning faster, indicating uncertainty about the relationship between angular momentum and angular velocity.
  • Several participants assert that angular velocity, not angular momentum, determines the speed of spin, emphasizing that angular momentum is influenced by both moment of inertia and angular velocity.
  • Participants clarify that the moment of inertia must be considered, as it varies between different objects, which affects the conclusions that can be drawn about their angular velocities.
  • One participant corrects a previous statement regarding angular momentum, highlighting the importance of precise terminology in the discussion.
  • Another participant explicitly states that the conclusion about spinning speed can only be made if the objects in question have the same moment of inertia.

Areas of Agreement / Disagreement

Participants generally agree that angular velocity is the determining factor for how fast an object spins, and that angular momentum alone does not provide sufficient information without considering moment of inertia. However, there is some initial confusion regarding the relationship between these concepts.

Contextual Notes

The discussion does not resolve the initial question posed, as it remains contingent on the definitions and conditions related to moment of inertia and the specific objects being compared.

avito009
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If a top has angular momentum of 12 units and the Earth has angular momentum of 100. Does this mean that Earth is spinning faster than the top since it has more angular momentum? The answer is there at the back of my head but can't articulate it.
 
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No. Angular velocity tells you what spins faster.
 
No. Angular momentum ( its magnitude) is the product of moment of inertia and the angular velocity. In your case the rotational inertia of the Earth and the top aren't equal, so you can't make the conclusion as you did.
 
Last edited:
Aniruddha@94 said:
No. Angular velocity ( its magnitude) is the product of moment of inertia and the angular velocity. In your case the rotational inertia of the Earth and the top aren't equal, so you can't make the conclusion as you did.

A typo, there, it's Angular Momentum that you meant.
 
sophiecentaur said:
A typo, there, it's Angular Momentum that you meant.
Aah yes, sorry.. I'll edit it. Thanks.
 
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As everyone else has said, the answer is no. You could only draw the conclusion you draw if the objects are the same (same mass and distribution of mass). To be more precise, the moment of inertia needs to be the same. I think you could draw this conclusion from other posts, but I just wanted to be explicit.
 

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