A student (was 65.0 kg) is standing on a rotating platform (mass 145 kg). Treat

Question

A student (was 65.0 kg) is standing on a rotating platform (mass 145 kg). Treat the platform as a uniform cylinder with a radius of r=1.40 m and treat the student as a point object throughout the problem. The student is standing right on the edge. The platform starts at rest. A friend then exerts a constant torque on the platform of 220 N*m over a time of 3.00 s, at which point the friend stops pushing on the platform.

a. ) What is the angular acceleration of the platform while the friend is pushing?
b.) Waht is the angular velocity of the platform after the friend pushes for 3.00 s?
c.) What is the angular velocity of the platform atfter the friend pushes for 3.00s?
d.) After the friend stops pushing, the student walks to the very center of the platform (right on top of the axis). Assume that there is no net external torque acting on the platform while the student is moving, what is the new angular velocity of the platform?
e.) If the friend exerts a force right at the edge and tangential to the platform when getting the platform up to speed as described above, what is the force that the friend applies to the platform?

Explanation / Answer

(A) torque = I alpha

I = (145 x 1.40^2 / 2) + (65 x 1.40^2) = 269.5 kg m^2

putting in,

220 = 269.5 alpha

alpha = 0.816 rad/s^2 ......Ans

(B) w = wi + alpha t

w = 0 + (0.816 x 3)

w = 2.45 rad/s

(c) w = 2.45 rad/s

(d) Applying angular momentum conservation,

269.5 x 2.45 = (145 x 1.40^2 / 2) wf

wf = 4.64 rad/s

(e) torque = r F

220 = 1.40 F

F =157.14 N ....Ans

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