1. ConcepTest 7.1aBonnie and Klyde I Bonnie Klyde Bonnie sits on the outer rim of a merry-go-round, and Klyde sits midway between the center and the rim. The merry-go-round makes one complete revolution every two seconds. Klyde’s angular velocity is: a) same as Bonnie’s b) twice Bonnie’s c) half of Bonnie’s d) 1/4 of Bonnie’s e) four times Bonnie’s

2. angular velocity  is the same The angular velocity  of any point on a solid object rotating about a fixed axis is the same. Both Bonnie & Klyde go around one revolution (2  radians) every two seconds. ConcepTest 7.1aBonnie and Klyde I Bonnie Klyde Bonnie sits on the outer rim of a merry-go-round, and Klyde sits midway between the center and the rim. The merry-go-round makes one complete revolution every two seconds. Klyde’s angular velocity is: a) same as Bonnie’s b) twice Bonnie’s c) half of Bonnie’s d) 1/4 of Bonnie’s e) four times Bonnie’s

3. ConcepTest 7.1bBonnie and Klyde II Bonnie Klyde a) Klyde b) Bonnie c) both the same d) linear velocity is zero for both of them Bonnie sits on the outer rim of a merry- go-round, and Klyde sits midway between the center and the rim. The merry-go-round makes one revolution every two seconds. Who has the larger linear (tangential) velocity?

4. linear speeds v v = R  Bonnie is located further out Their linear speeds v will be different since v = R  and Bonnie is located further out (larger radius R) than Klyde. Bonnie Klyde a) Klyde b) Bonnie c) both the same d) linear velocity is zero for both of them Bonnie sits on the outer rim of a merry- go-round, and Klyde sits midway between the center and the rim. The merry-go-round makes one revolution every two seconds. Who has the larger linear (tangential) velocity? ConcepTest 7.1bBonnie and Klyde II

5. Suppose that the speedometer of a truck is set to read the linear speed of the truck, but uses a device that actually measures the angular speed of the tires. If larger diameter tires are mounted on the truck instead, how will that affect the speedometer reading as compared to the true linear speed of the truck? a) speedometer reads a higher speed than the true linear speed b) speedometer reads a lower speed than the true linear speed c) speedometer still reads the true linear speed ConcepTest 7.2 Truck Speedometer

6. Suppose that the speedometer of a truck is set to read the linear speed of the truck, but uses a device that actually measures the angular speed of the tires. If larger diameter tires are mounted on the truck instead, how will that affect the speedometer reading as compared to the true linear speed of the truck? a) speedometer reads a higher speed than the true linear speed b) speedometer reads a lower speed than the true linear speed c) speedometer still reads the true linear speed The linear speed is v =  R. So when the speedometer measures the same angular speed  as before, the linear speed v is actually higher, because the tire radius is larger than before. ConcepTest 7.2 Truck Speedometer

7. An object at rest begins to rotate with a constant angular acceleration. If this object rotates through an angle  in the time t, through what angle did it rotate in the time 1/2 t? a) 1/2  b) 1/4  c) 3/4  d) 2  e) 4  ConcepTest 7.3aAngular Displacement I

8. An object at rest begins to rotate with a constant angular acceleration. If this object rotates through an angle  in the time t, through what angle did it rotate in the time 1/2 t? a) 1/2  b) 1/4  c) 3/4  d) 2  e) 4  half the timeone-quarter the angle The angular displacement is  = 1/2  t 2 (starting from rest), and there is a quadratic dependence on time. Therefore, in half the time, the object has rotated through one-quarter the angle. ConcepTest 7.3aAngular Displacement I

9. An object at rest begins to rotate with a constant angular acceleration. If this object has angular velocity  at time t, what was its angular velocity at the time 1/2 t? a) 1/2  b) 1/4  c) 3/4  d) 2  e) 4  ConcepTest 7.3bAngular Displacement II

10. An object at rest begins to rotate with a constant angular acceleration. If this object has angular velocity  at time t, what was its angular velocity at the time 1/2t? a) 1/2  b) 1/4  c) 3/4  d) 2  e) 4  half the time half the speed The angular velocity is  =  t (starting from rest), and there is a linear dependence on time. Therefore, in half the time, the object has accelerated up to only half the speed. ConcepTest 7.3bAngular Displacement II

11. The fan blade is slowing down. What are the signs of a. b. c. d.

12. The fan blade is slowing down. What are the signs of a. b. c. d.

13. A wheel rotating at the rate of 5 rev/s has what approximate angular velocity? a) 3.2 rad/s b) 1.6 rad/s c) 16 rad/s d) 31 rad/s

14. A wheel rotating at the rate of 5 rev/s has what approximate angular velocity? a) 3.2 rad/s b) 1.6 rad/s c) 16 rad/s d) 31 rad/s

15. Consider a child who is swinging. As she reaches the lowest point in her swing a) the tension in the rope is equal to her weight. b) the tension in the rope is equal to her mass times her acceleration. c) her acceleration is downward at 9.8 m/s 2. d) none of these choices will occur.

16. Consider a child who is swinging. As she reaches the lowest point in her swing a) the tension in the rope is equal to her weight. b) the tension in the rope is equal to her mass times her acceleration. c) her acceleration is downward at 9.8 m/s 2. d) none of these choices will occur.

17. A rigid object is rotating with an angular speed ω < 0. The angular velocity vector ω and the angular acceleration vector α are antiparallel. The angular speed of the rigid object is a) clockwise and increasing b) clockwise and decreasing c) counterclockwise and increasing d) counterclockwise and decreasing

18. A rigid object is rotating with an angular speed ω<0. The angular velocity vector ω and the angular acceleration vector α are antiparallel. The angular speed of the rigid object is a) clockwise and increasing b) clockwise and decreasing c) counterclockwise and increasing d) counterclockwise and decreasing The fact that ω is negative indicates that we are dealing with an object that is rotating in the clockwise direction. We also know that when ω and α are antiparallel, ω must be decreasing – the object is slowing down. Therefore, the object is spinning more and more slowly (with less and less angular speed) in the clockwise, or negative, direction.