一、轉動（第十、十一章）

Examples:

5. If a wheel is turning at 3.0 rad/s, the time it takes to complete one revolution is about:

A. 0.33 s

B. 0.67 s

C. 1.0 s

D. 1.3 s

E. 2.1 s

ans: E

7. The angular speed of the second hand of a watch is:

A. (π/1800) rad/s

B. (π/60)m/s

C. (π/30)m/s

D. (2π)m/s

E. (60)m/s

ans: C

2. The directionality of angular variables, such as ω, α, τ or L

Examples:

17. A wheel initially has an angular velocity of −36 rad/s but after 6.0 s its angular velocity is −24 rad/s. If its angular acceleration is constant the value is:

A. 2.0 rad/s²

B. −2.0 rad/ s²

C. 3.0 rad/ s²

D. −3.0 rad/ s²

E. −6.0 rad/ s²

ans: A

25. If the angular velocity vector of a spinning body points out of the page then, when viewed from above the page, the body is spinning:

A. clockwise about an axis that is perpendicular to the page

B. counterclockwise about an axis that is perpendicular to the page

C. about an axis that is parallel to the page

D. about an axis that is changing orientation

E. about an axis that is getting longer

ans: B

Examples:

9. A sphere and a cylinder of equal mass and radius are simultaneously released from rest on the same inclined plane and roll without sliding down the incline. Then:

A. the sphere reaches the bottom first because it has the greater inertia

B. the cylinder reaches the bottom first because it picks up more rotational energy

C. the sphere reaches the bottom first because it picks up more rotational energy

D. they reach the bottom together

E. none of the above are true

ans: E

11. A hoop rolls with constant velocity and without sliding along level ground. Its rotational kinetic energy is:

A. half its translational kinetic energy

B. the same as its translational kinetic energy

C. twice its translational kinetic energy

D. four times its translational kinetic energy

E. one-third its translational kinetic energy

ans: B

53. When a thin uniform stick of mass M and length L is pivoted about its midpoint, its rotational inertia is ML²/12. When pivoted about a parallel axis through one end, its rotational inertia is:

A. ML²/12

B. ML²/6

C. ML²/3

D. 7ML²/12

E. 13ML²/12

ans: C

Examples

35. A 2.0-kg stone is tied to a 0.50-m long string and swung around a circle at a constant angular velocity of 12 rad/s. The net torque on the stone about the center of the circle is:

A. 0

B. 6.0N · m

C. 12N · m

D. 72N · m

E. 140N · m

ans: A

36. A 2.0-kg stone is tied to a 0.50-m long string and swung around a circle at a constant angular velocity of 12 rad/s. The circle is parallel to the xy plane and is centered on the z axis, 0.75m from the origin. The magnitude of the torque about the origin is:

A. 0

B. 6.0N · m

C. 14N · m

D. 72N · m

E. 108N · m

ans: E

Examples

24. A 6.0-kg particle moves to the right at 4.0m/s as shown. The magnitude of its angular momentum about the point O is:

A. zero

B. 288 kg · m²/s

C. 144 kg · m²/s

D. 24 kg · m²/s

E. 249 kg · m²/s

ans: C

31. A uniform disk has radius R and mass M. When it is spinning with angular velocity ω about an axis through its center and perpendicular to its face its angular momentum is Iω. When it is spinning with the same angular velocity about a parallel axis a distance h away its angular momentum is:

A. Iω

B. (I +Mh²)ω

C. I − M h²)ω

D. (I +MR²)ω

E. (I −MR²)ω

ans: B

Examples:

34. A rod rests on frictionless ice. Forces that are equal in magnitude and opposite in direction are then simultaneously applied to its ends as shown. The quantity that vanishes is its:

A. angular momentum

B. angular acceleration

C. total linear momentum

D. kinetic energy

E. rotational inertia

ans: C

41. An ice skater with rotational inertia I is spinning with angular speed ω. She pulls her arms in, thereby increasing her angular speed to 4ω. Her rotational inertia is then:

A. I

B. I/2

C. 2I

D. I/4

E. 4I

ans: D