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 0.0650 m, an angular speed of 82.0 rad/s, and a moment of inertia of 1.05 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 3.00 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

Initial angular speed   1 = 82.0 rad/s,

Final speed 2 = 1/4=20.5 rad/s

time t = 3 s

radius r = 0.0650 m,

moment of inertia   I = 1.05 kg·m2

a)

The magnitude of the angular deceleration of the cylinder   = (1- 2)/t

= (82.0- 20.5) / 3 rad/s2

= 20.5 rad/s2

b)

torque = I = rF

F = I/r= (1.05 kg·m2) x (20.5 rad/s2)/0.0650

solving we get   frictional force F = 331.153 N

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