3 3p Two wheels A and B are connected by a belt assume that

3. (3p.) Two wheels, A and B, are connected by a belt (assume that the belt does not sleep). The radius of B is four times the radius of A. What would be the ratio of rotational inertias IB/IA, if a) both wheels have the same angular momenta; b) both wheels have the same rotational kinetic energy?

Solution

Since they are connected by same belt the velocity of outer rim for both wheels will be same. Now outer rim velocity is given by wheels angular velocity multiplied by its radius so angular velocity of wheel A is four times that of wheel B.

A) angular momentum is the product of rotational inertia and angular velocity so IB/IA=4

B)rotational kinetic energy is the product of rotational inertia and square of angular velocity so IB/IA=16