3.A lazy Susan consists of a heavy plastic disk mounted on a frictionless bearin

Question

3.A lazy Susan consists of a heavy plastic disk mounted on a frictionless bearing resting on a vertical shaft through its center. The cylinder has a radius R = 10 cm and mass M = 0.39 kg. A cockroach (mass m = 0.015 kg) is on the lazy Susan, at a distance of 10cm from the center. Both the cockroach and the lazy Susan are initially at rest. The cockroach then walks along a circular path concentric with the axis of the lazy Susan at a constant distance of 10 cm from the axis of the shaft. If the speed of the cockroach with respect to the lazy Susan is 0.01 m/s, what is the speed of the cockroach with respect to the room?

4.The figure below shows a thin, uniform bar of length D = 1.05 m and mass M = 0.66 kg pivoted at the top. The rod, which is initially at rest, is struck by a particle whose mass is m = 0.30 kg at a point x = 0.80d below the pivot. Assume that the particle sticks to the rod. If the maximum angle between the rod and the vertical following the collision is 60

Explanation / Answer

3)

here , let the angular speed of susan is w ,

Now, as there is no external torque acting on the system ,

Using conservation of angular momentum ,

I * w - m* r * (v - r *w) = 0

0.5 * 0.39 * 0.10^2 * w - 0.015 * 0.10 * (0.01 - 0.10 * w) = 0

solving for w ,

w = 0.00714 rad/s

speed of the cockroach with respect to the room = 0.01 - 0.00714 * 0.10

speed of the cockroach with respect to the room = 0.00929 m/s

speed of the cockroach with respect to the room is 9.29 *10^-3 m/s

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