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 0.0700 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 5.60 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

thanks

Explanation / Answer

Radius of the cyllinder is r = 0.0700m Angular speed of the cyllinder is = 88.0 rad /s Moment of inertia is I = 0.850 kg m^2 The frictional force reduces angular speed of the cylinder   during a time t = 5.60 s. a ) Angular deceleration is = / t                                              = 88.0 rad / s / 5.60s                                              = 15.7 rad/ s^2 b )
magnitude of the force of friction applied by the brake shoe is     F_fr = I^2 / r            = 0.850 kg m^2 * ( 88.0rad/s)^2 / 0.0700m          = 9.40*10^4 N

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