Rotational

• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• A radian is about:

  A. 25◦

  B. 37◦

  C. 45◦

  D. 57◦

  E. 90◦

  D
• One revolution per minute is about:

  A. 0.0524 rad/s

  B. 0.105 rad/s

  C. 0.95 rad/s

  D. 1.57 rad/s

  E. 6.28 rad/s

  B
• The figure shows a cylinder of radius 0.7 m rotating about its axis at 10 rad/s. The speed of the point P is:

  A. 7.0 m/s

  B. 14π rad/s

  C. 7.0π rad/s

  D. 0.70 m/s

  E. none of these

  A
• The fan shown has been turned on and is now slowing as it rotates clockwise. The direction of the acceleration of the point X on the fan tip could be:

  A. Xuong trai

  B. Xuong phai

  C. Xuong giua

  D. Sang trai

  E. Sang phai

  D
• A wheel of diameter 3.0 cm has a 4.0-m cord wrapped around its periphery. Starting from rest,

  the wheel is given a constant angular acceleration of 2.0 rad/s

  2

  . The cord will unwind in:

  A. 0.82 s

  B. 2.0 s

  C. 8.0 s

  D. 16 s

  E. 130 s

  D
• A particle moves in a circular path of radius 0.10 m with a constant angular speed of 5 rev/s.

  The acceleration of the particle is:

  A. 0.10π m/s^2

  B. 0.50 m/s^2

  C. 500π m/s^2

  D. 1000π2 m/s^2

  E. 10π2 m/s^2

  E
• Wrapping paper is being from a 5:0-cm radius tube, free to rotate on its axis. If it is pulled at

  the constant rate of 10 cm=s and does not slip on the tube, the angular velocity of the tube is:

  A. 2:0 rad/s

  B. 5:0 rad/s

  C. 10 rad/s

  D. 25 rad/s

  E. 50 rad/s

  A
• String is wrapped around the periphery of a 5.0-cm radius cylinder, free to rotate on its axis.

  The string is pulled straight out at a constant rate of 10 cm/s and does not slip on the cylinder.

  As each small segment of string leaves the cylinder, its acceleration changes by:

  A. 0

  B. 0.010 m/s^2

  C. 0.020 m/s^2

  D. 0.10 m/s^2

  E. 0.20 m/s^2

  E
• For a wheel spinning with constant angular acceleration on an axis through its center, the ratio

  of the speed of a point on the rim to the speed of a point halfway between the center and the

  rim is:

  A. 1

  B. 2

  C. 1/2

  D. 4

  E. 1/4

  B