Chapter 09, Problem 37 Interactive Solution 9.37 at www.wiley.com/college/cutnel

Question

Chapter 09, Problem 37 Interactive Solution 9.37 at www.wiley.com/college/cutnell presents a method for modeling this problem. Multiple-Concept 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 0.130 m, an angular speed of 56.0 rad/s, and a moment of inertia of 1.07 kg-m2. A brake shoe presses against the surface of the cylinder and applies a tangentia frictional force to it. The frictional force reduces the angular speed of the cylinder by a factor of 9 during a time of 4.00 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. (a) Number Units (b) Number Units By accessing this Question Assistance, you will learn while you earn points based on the Point Potential Policy set by your instructor

Explanation / Answer

a) initial angular speed, wi = 56 rad/s

final angular speed, wf = 56/9 = 6.22 rad/s

Using wf = wi + alpha*t

6.22 = 56 + alpha*4

alpha = - 12.44 rad/s^2

( if final speed is 56 - 9 = 47 rad/s then alpha = - 2.25 rad/s^2)

B) Using torque = I x alpha

r f = I alpha

0.130 f = 1.07 (12.44)

f = 102.39 N

(for other case, f = (1.07 x 2.25 / 0.130) = 18.52 N )

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51.

energy of rotating disk = I w^2 /2

= ( m r^2 / 2) ( w^2) /2

hence,

2.91 x 10^9 = (7.35 x 0.204^2 /2 ) (w^2 / 2)

w = 195075.47 rad/s = 1495075.47 x 60 / 2pi rev/min

w = 1862833.48 rev/min

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