A uniform disk with mass 39.4 kg and radius 0.200 m has an axle through its cent

Question

A uniform disk with mass 39.4 kg and radius 0.200 m has an axle through its center and can rotate without friction. Starting from rest, a constant force 31.5 N is applied tangentially at the rim of the disk (visualize a hand pushing a bicycle wheel to get it spinning, but imagine that the force is applied constantly as the wheel speeds up, causing it to accelerate its rotation).

A) Compute the magnitude v of the tangential velocity of a point on the rim of the disk after the disk has turned through 0.350 revolution.

Explanation / Answer

Torque = F*R = I*alpha = MR^2/2*alpha

=> 31.5*0.2 = 39.4*0.2^2)/2*alpha

=> alpha = 7.994 rad/s^2

W^2 = W0^2 + 2*alpha*thetha

=> W^2 = 0 + 2*7.994*0.350*2*3.14

=> W = 5.928 rad/s

V = WR = 5.928*.2 = 1.185 m/s

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