A cylinder is rotating about an axis that passes through the center of each circ

Question

A cylinder is rotating about an axis that passes through the center of each circular end piece. The cylinder has a radius of 0.150 m, an angular speed of 64.0 rad/s, and a moment of inertia of 0.729 kg·m2. A brake shoe presses against the surface of the cylinder and applies a tangential frictional force to it. The frictional force reduces the angular speed of the cylinder by a factor of 4 during a time of 7.00 s. (a) Find the magnitude of the angular deceleration of the cylinder. (b) Find the magnitude of the force of friction applied by the brake shoe.

Explanation / Answer

A. wi = 64.0 rad/sec

wf = 64/4 = 16 rad/sec

wf = wi + alpha*t

alpha = (wf - wi)/t

alpha = (16 - 64)/7 = -6.857 rad/sec^2

B. on the one hand

torque = I*alpha

on the other side

torque = Ft*R

I = 0.729 kg-m^2

alpha = -6.857 rad/sec^2

negative sign means its a de-acceleration

R = 0.15

Ft*R = I*alpha

Ft =I*alpha/R

Ft = 0.729*6.857/0.15 = 33.32 N

Let me know if you have any doubt.

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