A grinding wheel that has a mass of 62.0 kg and a radius of 0.560 m is rotating

Question

A grinding wheel that has a mass of 62.0 kg and a radius of 0.560 m is rotating at 74.0 rad/s. (The wheel can be modeled as a disk and assume it rotates without friction on its axis)

a) What is the moment of inertia of the grinding wheel?

b) A brake is applied to the outer edge with a force of 43 N. What is the resulting torque?

c) What is the resulting angular acceleration of the grinding wheel?

d) How much time passes until the wheel comes to a stop?

e) How many revolutions does the wheel go through as it comes to a stop?

Explanation / Answer

a)moment of inertia,I = .5*62*.56^2 = 9.72 kg.m^2 b)torque,t = F*r = 43*.56= 24.08 N.m c) a = t/I = 2.48 rad/s2 d) time taken = 74/(2.48) =29.9 s e)no of revolutions = 74^2/(2*2.48) =175.7 rotations

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