A uniform disk with mass 39.1 kg and radius 0.230 m has an axle through its cent

Question

A uniform disk with mass 39.1 kg and radius 0.230 m has an axle through its center and can rotate without friction. Starting from rest, a constant force 30.5 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, causeing it to accelerate its rotation). Compute the magnitude v of the tangential velocity of a point on the rim of the disk after the disk has turned through 0.260 revolution. Express your answer with the appropriate units.

Explanation / Answer

torque T = I*alpha

alpha = r*f/1/2mr^2 = 2f/mr

alpha = 2*30.5/39.1*0.23 = 6.78 rad/s^2

wf^2 = wi^2+2alpha*theta

wf = sqrt(2*6.78*0.26*2*3.14)

wf = 4.71 rad/s

v = rw

v = 0.23*4.71 = 1.08 m/s

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