Interactive Solution 9.37 at presents a method for modeling this problem. Multip

Question

Interactive Solution 9.37 at presents a method for modeling this problem. Multiple-Conceot Example 10 offers useful background for problems like this one. A cylinder is rotating about an axis that passes through the center of each circular end piece. The cylinder has a radius of 0.0770 m, an angular speed of 66.0 rad/s, and a moment of inertia of 0.936 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 3 during a time of 2.00 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) so w = w0 + alpha t

22 = 66 + alpha*2

2 alpha = -44

alpha = -22 rad/s^2

so in mag = 22 rad/s^2

b) torque = I alpha

but torque = r F

F = Ialpha/r = 0.936*22/0.077= 267.4 N

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