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 0.0550 m, an angular speed of 88.0 rad/s, and a moment of inertia of 0.850 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 two during a time of 4.20 s.
(a) Find the magnitude of the angular deceleration of the cylinder.
__________ rad/s2

(b) Find the magnitude of the force of friction applied by the brake shoe.

_____________ N

Explanation / Answer

intial angular speed   1 = 88.0 rad/s , final 2 = 44 rad/s

time t = 4.2 s

radius r = 0.0550 m ,

moment of inertia   I = 0.850 kg·m2

a)

the magnitude of the angular deceleration of the cylinder   = 2 -1/t = 10.476 rad/s2

b)

torque = I = rF

F = I/r

solving we get   frictional force F = 161.9 N

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