Wheels A and B differ only in the values of their mass moments of inertia. Carefully read the question to understand the distribution of mass for each wheel.
- For wheel A, all mass is concentrated at a point at its center (a PARTICLE). The spokes and rim only serve to support the particle and effectively add no mass or mass moment of inertia to the wheel.
- For wheel B, all mass is distributed around the hoop (a THIN RING for which the mass moment of inertia is given in an appendix in the textbook).
3 comments:
My solution shows that V_a = V_b/sqrt(2). My intuition says that B should have more momentum.. is it true that B will be harder to stop, even though it's not accelerating as fast as A?
Your conclusion is correct: all of the original potential energy for A goes into translational energy, whereas the same PE for B goes into both translational and rotational energy. Therefore, B is moving more slowly than A.
For the same translational speed, B will require more force to stop than A over the same amount of time.
Great. Thank you.
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