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aigerimzh

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1. Homework Statement

A ring of mass M and radius R lies on its side on a frictionless table. It is pivoted to the table at its rim. A bug of mass m walks around the ring with speed v, starting at the pivot. What is the rotational velocity of the ring when the bug (a) is halfway around and (b) back at the pivot?

2. Homework Equations

p=mv

3. The Attempt at a Solution

If I assume that only momentum and angular momentum are conserved, and that the bug still has speed v with respect to the ring, I get these equations:

-mv = m(v + V) + Mv

-mRv = -mR(v + V) + M(R^2)(omega)

where V is the velocity of the ring and omega is the angular velocity. I solve these equations for omega, and I don't get the answer in the book.

Where did I go wrong? Thanks in advance for all your help.

A ring of mass M and radius R lies on its side on a frictionless table. It is pivoted to the table at its rim. A bug of mass m walks around the ring with speed v, starting at the pivot. What is the rotational velocity of the ring when the bug (a) is halfway around and (b) back at the pivot?

2. Homework Equations

p=mv

3. The Attempt at a Solution

If I assume that only momentum and angular momentum are conserved, and that the bug still has speed v with respect to the ring, I get these equations:

-mv = m(v + V) + Mv

-mRv = -mR(v + V) + M(R^2)(omega)

where V is the velocity of the ring and omega is the angular velocity. I solve these equations for omega, and I don't get the answer in the book.

Where did I go wrong? Thanks in advance for all your help.

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