(13 pts) A student (mass=65.0 kg) is standing on a rotating platform (mass=115 k

Question

(13 pts) A student (mass=65.0 kg) is standing on a rotating platform (mass=115 kg). Treat the platform as a uniform cylinder with a radius 1.20 m, and treat the student as a point object. The student is standing right on the edge. The platform starts at rest. A friend then exerts a constant torque On the platform. This causes the angular speed of the platform to increase to 0.672 rad/s over a time of 4.60 S, at which point in the time the friend stops pushing the platform. What is the moment of inertia of the combination of the platform and the student while the student is standing at the edge of the platform? Answer: What constant torque must the friend apply in order to get the platform moving at the angular speed described above? Answer: (c) (5 pts) After the friend stops pushing, the student walks to the center of the platform. What is the angular speed of the platform when the student reaches the center?

Explanation / Answer

4) a) Moment of inertia I = MR^2 /2 + mR^2

I = 115 x 1.20^2 /2 + 65 x 1.20^2

I = 176.4 kg.m^2

b) alpha = 0.672 / 4.60 = 0.146 rad/s2

torque = Ix alpha = 176.4 x 0.146 = 25.77 Nm

C) using angular momentum conservation,

I1w1 = I2w2

(115 x 1.20^2 /2 + 65 x 1.20^2 ) x 0.672 = (115 x 1.20^2 /2 + 0 )w

w = 1.43 rad / s

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