1. A bug is crawling around the circumference of a circle of radius 46 cm. You place a stone at the position of the bug when you start your stopwatch (at t = 0.0 s). At the time t = 145 s, you note that the bug has crawled 127 cm measured around the edge of the circle from the stone. (a) What is the bug’s average tangential speed (the same as the tangential velocity)? (b) What is the bug’s average angular velocity? (c) Through what angle (in radians) has the bug crawled as viewed from the center of the circle?
2. When turned on, the CD in a CD-player speeds up from rest to a final angular velocity of 3.50 rev/s in a time of 1.1 s. (a) Express the given final angular velocity in units of rad/s. (b) What was the average angular acceleration of the CD? (c) What was the average tangential acceleration of a mark on the outer rim of the compact disk if the CD has a diameter of 12 cm?
3. You find experimentally that a meter stick balances on your right-hand index finger at the 50.7-cm mark. Once balanced, you use your left-hand index finger to exert a force of 0.23 N at the 33.0-cm mark. (a) What is the location of the axis of rotation of the meter stick? (b) What is the moment arm of the force you exert with your left-hand index finger about the axis? (c) What is the magnitude of the torque this force exerts? (d) What mass (in grams) would you have to place at the 33.0-cm mark on the meter stick to result in the same torque as that exerted by your finger?
II. Some Standards
4. A moth is flying in a horizontal circle of radius 1.2 m with a constant speed. It takes the moth 1.0 min to fly around the circle 4 times. (a) What is the period of the moth’s motion? (b) What is the linear frequency of the moth’s motion? (c) What is the angular velocity of the moth around the circle? (d) What is the moth’s tangential speed? (e) What is the moth’s centripetal acceleration? (f) What is its tangential acceleration? (g) How long does it take for the moth to fly through an angle of 57o as viewed from the center of the circle?
5. A stock car drives around a circular track of radius 150 m. Starting from rest and accelerating uniformly, it takes 45 s for the car to reach a speed of 30.0 m/s. (a) What is the angular velocity of the car at the end of the 45-s interval? (b) What is the car’s angular acceleration? (c) What is the final angular displacement of the car after the 45-s interval? (d) How far did the car travel during this interval? (e) What is the car’s tangential acceleration? (f) What is the car’s centripetal acceleration at the end of the interval? (g) What is the car’s total magnitude of acceleration at this time? (Note: The centripetal and tangential accelerations can be thought of as two perpendicular components of the car’s acceleration. How do you find the magnitude of a vector when you know its two perpendicular components?) (h) What is the direction of the car’s total acceleration vector relative to the centripetal direction? (i) How long would it take for the car to complete its first lap around the track if its acceleration remains constant?
III. So, you think you’re pretty good...?
6. A yo-yo of mass 120 g is unwinding its way down a vertical string of length 1.1 m , as shown in the figure. Its angular acceleration about its axis 
as it’s spinning downward is 0.78 rad/s2. The radius of the inner spool about which the string is wound is 3.1 cm. (a) What is the linear acceleration of the descending yo-yo? (b) How long does it take the yo-yo to reach the bottom of the string if it starts from rest with 5.2 cm of the string already unwound? (That is, the vertical part of the string shown in the figure is 5.2 cm when the yo-yo starts unwinding.) (c) What is the final angular velocity of the yo-yo when it reaches the bottom of the string? (d) As the yo-yo is unwinding, what is the torque exerted by the weight of the yo-yo about the yo-yo’s axis? (e) What is the tension in the string? (Hint: See part a and a FBD....) (f) What is the torque about the axis of the yo-yo exerted by the tension in the string?
7. A 210-g meter stick is nailed to a wall at its 30-cm mark. The meter stick is free to rotate about this nail (it is not nailed tightly!). Three forces of magnitudes F1 = 5.3 N, F2 = 7.5 N and F3 = 12 N act as shown in the figure, with q2 = 35o and q3 = 79o. Let the positive direction of rotation for torques be CW. Find (a) the moment arm for the force F1. (b) the moment arm for the force F2. (c) the moment arm for the force F3. (d) the torque exerted by F1 about the axis of rotation. (e) the torque exerted by F2. (f) the torque exerted by F3. (g) What is the torque exerted by the meter stick’s weight? (h) What is the net torque exerted on the meter stick? (i) Which way would the meter stick start rotating from rest as a result of these torques?
8. The right-angle guide shown below experiences three forces of magnitudes FA = 12 N, FB = 16 N and FC = 9.4 N. The directions of the forces are as shown, with qC = 42o. Let the positive direction of rotation for torques be CW. About the axis of rotation shown, what is (a) the torque exerted by the force FA? (b) the torque exerted by FB ? (c) the torque exerted by FC? (d) What is the sum of these torques? (e) In what direction would the guide rotate from rest as a result of these three torques only?
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