Chapter 11 Kinematics: Angular Motion

 Pay careful attention to sign convention of both given data and calculated values. If initial velocity or displacement is positive, then acceleration is positive and deceleration is negative.

· For a rotating object:

· If angular velocity is zero,  an = 0 but  at may be present.

· If angular acceleration is zero,  at = 0 but  an may be present.

Section: Problems

· 11-1 The minute hand of a clock travels from the 12 to the 9, whereupon it is discovered that the clock is fast. The minute hand is turned back and now points at the 6. What is the angular distance and displacement of the hand in radians?

2p rad p rad

· 11-6 The handle of a winch is turned 70 revolutions in 1.5 minutes. Determine the angular speed in rad/s.

? = 4.89 rad/s

· 11-9 Starting from rest, a shaft accelerates uniformly to 800 rpm in 10 seconds. Determine the angular acceleration in rad/s2.

8.37 rad/s^2

· 11-12 A rotating drive shaft decelerates uniformly from 900 rpm to 650 rpm in 6 seconds. Determine the angular deceleration and the total number of revolutions in the 6-second interval.

4.36 rad/s^2 77.5 rev

· 11-17 A flywheel accelerates for 8 seconds at 1.3 rad/s2 from a speed of 40 rpm. Determine (a) the total number of revolutions and (b) the final angular speed.

12 rev 14.6 rad/s

· 11-27 For the system shown in Figure P11–27, determine the angular acceleration of the wheel and the tangential velocity of point A.

· 11-40 Pulleys C and D in Figure P11–40 are fastened together. Weights A and B are supported by ropes wound around the pulleys as shown. If weight A is accelerating downward at 2 m/s2, determine (a) the angular acceleration of pulleys C and D and (b) the linear acceleration of weight B.

· 11-53 A point 150 mm from the center of rotation has a normal acceleration of 4000 m/s2. Determine the speed of rotation.