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 52.0 rad/s, and a moment of inertia of 0.670 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 7 during a time of 9.00 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) the magnitude of the angular deceleration of the cylinder is:

w = wo + at
( 1/7 ) wo = wo + at
( 1/7 ) wo = wo + at
( 1/7 ) ( 52 rad / s ) = 52 + a ( 9.0 s )
a = - 4.95 rad /s^2

Hence magnitude of deacceleration is 4.95 rad/s^2.

b)the magnitude of the force of friction applied by the brake shoe is:

F*r = I*a

Here For is the friction force.
F ( 0.150 m ) = (0.670 kg m^2 ) ( 4.95 rad / s^2 )
F = 22 N

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