Chapter 10 Rotation

9. 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

B) the same as its translational kinetic energy

34. A wheel starts from rest and has an angular acceleration that is given by (t) = 6 rad/s4)t2. The angle through which it turns in time t is given by: A) [(1/8)t4] rad/s4 B) [(1/4)t4] rad/s4 C) [(1/2)t4] rad/s4 D) (t4) rad/s4 E) 12 rad

C) 1/2t^4 rad/s^4

. A wheel of radius 0.5 m rolls without sliding on a horizontal surface as shown. Starting from rest, the wheel moves with constant angular acceleration 6 rad/s2. The distance in traveled by the center of the wheel from t = 0 to t = 3 s is:

C) 13.5

11. A child, riding on a large merry-go-round, travels a distance of 3000 m in a circle of diameter 40 m. The total angle through which she revolves is: A) 50 rad B) 75 rad C) 150 rad D) 314 rad E) none of these

C) 150 rad d= ∅r ∅=d/r

39. A wheel starts from rest and has an angular acceleration of 4.0 rad/s2. When it has made 10 rev its angular velocity is: A) 8.9 rad/s B) 16 rad/s C) 22 rad/s D) 32 rad/s E) 250 rad/s

C) 22 rad/s

33. A wheel is spinning at 27 rad/s but is slowing with an angular acceleration that has a magnitude given by (3.0 rad/s4)t2. It stops in a time of: A) 1.7 s B) 2.6 s C) 3.0 s D) 4.4 s E) 9.0 s

C) 3.0s

36. A flywheel is initially rotating at 20 rad/s and has a constant angular acceleration. After 9.0 s it has rotated through 450 rad. Its angular acceleration is: A) 3.3 rad/s B) 4.4 rad/s C) 6.7 rad/s D) 11 rad/s E) 48 rad/s

C) 6.7 rad/s

10. When we apply the energy conversation principle to a cylinder rolling down an incline without sliding, we exclude the work done by friction because: A) there is no friction present B) the angular velocity of the center of mass about the point of contact is zero C) the coefficient of kinetic friction is zero D) the linear velocity of the point of contact (relative to the inclined surface) is zero E) the coefficient of static and kinetic friction are equal

C) the coefficient of kinetic friction is zero

9. The angular speed of the second hand of a watch is: A) (/1800) rad/s B) (/60) rad/s C) (/30) rad/s D) (2) rad/s E) (60) rad/s

C) w = 2pi/t pi/30 rad/sec

1. When a wheel rolls without slipping, A) its motion is purely translational. B) its motion is purely rotational. C) whether its motion is purely rotational or purely translational depends on whether it is rolling up or downhill. D) its motion is a combination of rotational and translational motion. E) every point on its rim has the same linear velocity

D)

29. The angular velocity of a rotating turntable is given in rad/s by ω(t) = 4.5 + 0.64t - 2.7t2. What is its average angular acceleration between t = 1.0 s and t = 3.0 s? A) 0.64 rad/s2 B) −5.4 rad/s2 C) −7.7 rad/s2 D) −10 rad/s2 E) −27 rad/s2

D) -10 rad/s^2

22. An object rotates from θ1 to θ2 through an angle that is less than π radians. Which of the following results in a positive angular displacement? A) θ1 = 45°, θ2= −45° B) θ1 = 45°, θ2= 15° C) θ1 = 45°, θ2= −45° D) θ1 = 135°, θ2= −135° E) θ1 = −135°, θ2= 135°

D) 135 degrees, -135 degrees

18. A wheel initially has an angular velocity of 18 rad/s. It has a constant angular acceleration of 2.0 rad/s2 and is slowing at first. What time elapses before its angular velocity is18 rad/s in the direction opposite to its initial angular velocity? A) 3.0 s B) 6.0 s C) 9.0 s D) 18 s E) 36 s

D) 18s

17. The angular velocity of a rotating wheel increases 2 rev/s every minute. The angular acceleration of this wheel is: A) 42 rad/s2 B) 2 rad/s2 C) 1/30 rad/s2 D) 2/30 rad/s2 E) 4 rad/s2

D) 2pi/30 rad/s^2

13. A flywheel rotating at 12 rev/s is brought to rest in 6 s. The magnitude of the average angular acceleration of the wheel during this process is: A) 1/ rad/s2 B) 2 rad/s2 C) 4 rad/s2 D) 4 rad/s2 E) 72 rad/s2

D) 4pi rad/s^2 α=ω/t 12rev/s/ 6s 2 rev/s^2 *2pi rad/rev 4pi rad/s^2

7. When the speed of a rear-drive car is increasing on a horizontal road the direction of the frictional force on the tires is: A) forward for all tires B) backward for all tires C) forward for the front tires and backward for the rear tires D) backward for the front tires and forward for the rear tires E) zero

D) backward for the front tires and forward for the rear tires

6. A forward force acting on the axle accelerates a rolling wheel on a horizontal surface. If the wheel does not slide the frictional force of the surface on the wheel is: A) zero B) in the forward direction and does zero work on the wheel C) in the forward direction and does positive work on the wheel D) in the backward direction and does zero work on the wheel E) in the backward direction and does positive work on the wheel

D) in the backward direction and does zero work on the wheel

14. A phonograph turntable, initially rotating at 0.75 rev/s, slows down and stops in 30 s. The magnitude of its average angular acceleration for this process is: A) 1.5 rad/s2 B) 1.5 rad/s2 C) /40 rad/s2 D) /20 rad/s2 E) 0.75 rad/s2

D) pi/20 rad/s^2 0.77/30 *2pi

10. The angular speed of the minute hand of a watch is: A) (60/) rad/s B) (1800/) rad/s C) () rad/s D) (/1800) rad/s E) (/60) rad/s

D) w= 2pi/3600 pi/1800 rad/s

6. An object rotates from θ1 to θ2 through an angle that is less than 2π radians. Which of the following represents its angular displacement? A) θ1 B) θ2 C) θ1 - θ2 D) θ2 - θ1 E) θ1 + θ2

D. 02-01

23. The coordinate of an object is given as a function of time by θ = 7t - 3t2, where θ is in radians and t is in seconds. Its average velocity over the interval from t = 0 to t = 2 s is: A) 5 rad/s B) -5 rad/s C) 11 rad/s D) -11 rad/s E) 1 rad/s

E) 1 rad/s v= x/t

40. A wheel starts from rest and has an angular acceleration of 4.0 rad/s2. The time it takes to make 10 revolutions is: A) 0.50 s B) 0.71 s C) 2.2 s D) 2.8 s E) 5.6 s

E) 5.6 s

8. If a wheel turning at a constant rate completes 100 revolutions in 10 s its angular speed is: A) 0.31 rad/s B) 0.63 rad/s C) 10 rad/s D) 31 rad/s E) 63 rad/s

E) 63 rad/s 100revs x 2pi divide by 10

2. A wheel rolls without slipping along a horizontal road as shown. The velocity of the center of the wheel is represented by . Point P is painted on the rim of the wheel. The direction of the instantaneous velocity of point P is: A) B) C) D) E) zero

E) Zero

11. Two uniform cylinders have different masses and different rotational inertias. They simultaneously start from rest at the top of an inclined plane and roll without sliding down the plane. The cylinder that gets to the bottom first is: A) the one with the larger mass B) the one with the smaller mass C) the one with the larger rotational inertia D) the one with the smaller rotational inertia E) neither (they arrive together)

E) neither (they arrive together)

8. A solid sphere and a solid cylinder of equal mass and radius are simultaneously released from rest on the same inclined plane 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 is true

E) none of the above

5. One-dimensional linear position is measured along a line, from a point designated x = 0. One-dimensional angular position: A) is measured along a line, from a point designated θ = 0. B) is measured along the axis of rotation. C) is the angle that an internal reference line makes with a fixed external reference line. D) is measured relative to the positive y axis. E) is meaningless, as rotations take place in two dimensions.

Is the angle that an internal reference line makes with a fixed external reference line

16. The angular velocity vector of a spinning body points out of the page. If the angular acceleration vector points into the page then: A) the body is slowing down B) the body is speeding up C) the body is starting to turn in the opposite direction D) the axis of rotation is changing orientation E) none of the above

a) the body is slowing down

4. Two wheels roll side-by-side without sliding, at the same speed. The radius of wheel 2 is twice the radius of wheel 1. The angular velocity of wheel 2 is: A) twice the angular velocity of wheel 1 B) the same as the angular velocity of wheel 1 C) half the angular velocity of wheel 1 D) more than twice the angular velocity of wheel 1 E) less than half the angular velocity of wheel 1

c) half the angular velocity of wheel 1

35. A wheel starts from rest and has an angular acceleration that is given by (t) = (6.0 rad/s4)t2. The time it takes to make 10 rev is: A) 1.3 s B) 2.1 s C) 2.8 s D) 3.3 s E) 4.0 s

d) 3.3s

21. The fan shown has been turned on and is slowing as it rotates clockwise. The direction of the acceleration of the point X on the fan tip could be: A) B) C) D) <--- E)

d) <---

27. Instantaneous angular speed is: A) total angular displacement divided by time B) the integral of the displacement over time C) the rate at which the angular acceleration is changing D) the magnitude of the instantaneous angular velocity E) a vector directed along the axis of rotation

d) the magnitude of the instantaneous angular velocity

7. 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

e) 2.1 seconds 2pi/3

21. Which of the following is a vector quantity? A) angular speed B) rotational inertia C) rotational kinetic energy D) mass E) torque

e) torque

37. A wheel rotates with a constant angular acceleration of rad/s2. During a certain time interval its angular displacement is rad. At the end of the interval its angular velocity is 2 rad/s. Its angular velocity at the beginning of the interval is: A) 0 rad/s B) 1 rad/s C) rad/s D) pisqrt 2 rad/s E) 2 rad/s

pi sqrt 2 rad/s

22. A particle moves along the x axis. In order to calculate the torque on the particle, you need to know: A) the velocity of the particle B) the rotational inertia of the particle C) the point about which the torque is to be calculated D) the kinetic energy of the particle E) the mass of the particle

the point about which torque is to be calculated

4. If a wheel turns with constant angular speed then: A) each point on its rim moves with constant velocity B) each point on its rim moves with constant acceleration C) the wheel turns through equal angles in equal times D) the angle through which the wheel turns in each second increases as time goes on E) the angle through which the wheel turns in each second decreases as time goes on

the wheel turns through equal angles in equal times

One revolution per minute is about:

0.105 rad/ sec 2pi÷60sec = 0.105

One revolution is the same as

2pi radians

A radian is about

57 degrees°

28. The angular velocity of a rotating turntable is given in rad/s by ω(t) = 4.5 + 0.64t - 2.7t2. What is its angular acceleration at t = 2.0 s? A) −10 rad/s2 B) -5.0 rad/s2 C) −5.4 rad/s2 D) 2.4 rad/s2 E) 3.1 rad/s2

A) -10 rad/s^2

The coordinate of an object is given as a function of time by θ = 7t - 3t2, where θ is in radians and t is in seconds. Its angular velocity at t = 3 s is: A) −11 rad/s B) −3.7 rad/s C) 1.0 rad/s D) 3.7 rad/s E) 11 rad/s

A) -11 rad/s

20. 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

A) 2 rad/s^2

12. Ten seconds after an electric fan is turned on, the fan rotates at 300 rev/min. Its average angular acceleration is: A) 3.14 rad/s2 B) 30 rad/s2 C) 30 rev/s2 D) 50 rev/min2 E) 1800 rev/s2

A) 3.14 rad/s^2 300 rev/min x 2pi x 1min/60sec = 31.4 rad/s a = w/t a = 31.4/10

38. A wheel initially has an angular velocity of 18 rad/s but it is slowing at a rate of 2.0 rad/s2. By the time it stops it will have turned through: A) 81 rad B) 160 rad C) 245 rad D) 330 rad E) 410 rad

A) 81 rad

12. A 5.0-kg ball rolls without sliding from rest down an inclined plane. A 4.0-kg block, mounted on roller bearings totaling 100 g, rolls from rest down the same plane. At the bottom, the block has: A) greater speed than the ball B) less speed than the ball C) the same speed as the ball D) greater or less speed than the ball, depending on the angle of inclination E) greater or less speed than the ball, depending on the radius of the ball

A) greater speed than the ball

A hoop, a uniform disk, and a uniform sphere, all with the same mass and outer radius, start with the same speed and roll without sliding up identical inclines. Rank the objects according to how high they go, least to greatest. A) hoop, disk, sphere B) disk, hoop, sphere C) sphere, hoop, disk D) sphere, disk, hoop E) hoop, sphere, disk

A) hoop, disk, sphere

30. This graph shows the angular velocity of a turntable as a function of time. What is its angular acceleration at t = 3.5 s? A) −10 rad/s2 B) −5 rad/s2 C) 0 rad/s2 D) 5 rad/s2 E) 10 rad/s2

A) −10 rad/s2

19. A wheel initially has an angular velocity of 36 rad/s but after 6.0s 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

B) -2 rad/s^2

25. This graph shows the angular position of an object as a function of time. What is its average angular velocity between t = 5 s and t = 9 s? A) 3 rad/s B) −3 rad/s C) 12 rad/s D) −12 rad/s

B) -3 rad/s

31. This graph shows the angular velocity of a turntable as a function of time. What is its average angular acceleration between t = 2 s and t = 4 s? A) −10 rad/s2 B) −5 rad/s2 C) 0 rad/s2 D) 5 rad/s2 E) 10 rad/s2

B) -5 rad/s^2

26. This graph shows the angular position of an object as a function of time. What is its instantaneous angular velocity at t = 1.5 s? A) −6 rad/s B) 6 rad/s C) 9 rad/s D) 12 rad/s E) Need additional information.

B) 6 rad/s

32. A wheel starts from rest and has an angular acceleration that is given by (t) = (6.0 rad/s4)t2. After it has turned through 10 rev its angular velocity is: A) 63 rad/s B) 75 rad/s C) 89 rad/s D) 130 rad/s E) 210 rad/s

B) 75 rad/s

15. 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

B) Counterclockwiese about an axis that is perpendicular to the page