Question 1

Complete the following statement: The angular measure 1.0 radian is equal to

Accepted Answer

A) 0.0175°. 
B) 57.3°. 
C) 1.57°. 
D) 3.14°. 
E) 6.28°.

Question 2

Which one of the following statements concerning a wheel undergoing rolling motion is true?

Accepted Answer

A) The angular acceleration of the wheel must be zero m/s2. 
B) The tangential velocity is the same for all points on the wheel. 
C) The linear velocity for all points on the rim of the wheel is non-zero. 
D) The tangential velocity is the same for all points on the rim of the wheel. 
E) There is no slipping at the point where the wheel touches the surface on which it is rolling.

Question 3

Which equation is valid only when the angular measure is expressed in radians?

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 4

A bicycle wheel of radius 0.70 m is rolling without slipping on a horizontal surface with an angular speed of 2.0 rev/s when the cyclist begins to uniformly apply the brakes. The bicycle stops in 5.0 s.
-Through how many revolutions did the wheel rotate during the 5.0 seconds of braking?

Accepted Answer

A) 10 rev 
B) 2.0 rev 
C) 9.6 rev 
D) 5.0 rev 
E) 0.4 rev

Question 5

A sculptor is sharpening a chisel on grindstone of radius 1.0 m that is spinning with a constant angular speed of 2.0 rad/s.
-What is the magnitude of the centripetal acceleration of a point on the rim of the grindstone?

Accepted Answer

A) zero m/s2 
B) 0.5 m/s2 
C) 1.0 m/s2 
D) 2.0 m/s2 
E) 4.0 m/s2

Question 6

A grindstone of radius 4.0 m is initially spinning with an angular speed of 8.0 rad/s. The angular speed is then increased to 12 rad/s over the next 4.0 seconds. Assume that the angular acceleration is constant.
-Through how many revolutions does the grindstone turn during the 4.0-second interval?

Accepted Answer

A) 0.64 
B) 3.8 
C) 4.0 
D) 6.4 
E) 40

Question 7

A fan rotating with an initial angular velocity of 1000 rev/min is switched off. In 2 seconds, the angular velocity decreases to 200 rev/min. Assuming the angular acceleration is constant, how many revolutions does the blade undergo during this time?

Accepted Answer

A) 10 
B) 20 
C) 100 
D) 125 
E) 1200

Question 8

A sculptor is sharpening a chisel on grindstone of radius 1.0 m that is spinning with a constant angular speed of 2.0 rad/s.
-What is the magnitude of the tangential acceleration of a point on the rim of the wheel?

Accepted Answer

A) zero m/s2 
B) 0.5 m/s2 
C) 1.0 m/s2 
D) 2.0 m/s2 
E) 4.0 m/s2

Question 9

A circular disk of radius 2.0 m rotates, starting from rest, with a constant angular acceleration of 20.0 rad/s2. What is the tangential acceleration of a point on the edge of the disk at the instant that its angular speed is 1.0 rev/s?

Accepted Answer

A) 40 m/s2 
B) 79 m/s2 
C) 110 m/s2 
D) 120 m/s2 
E) zero m/s2

Question 10

A long thin rod of length 2L rotates with a constant angular acceleration of 8.0 rad/s2 about an axis that is perpendicular to the rod and passes through its center.
-What is the ratio of the centripetal acceleration of a point on the end of the rod to that of a point a distance L/2 from the end of the rod?

Accepted Answer

A) 1:1 
B) 1:2 
C) 2:1 
D) 4:1 
E) 1:4

Question 11

What is the tangential speed of Nairobi, Kenya, a city near the equator? The earth makes one revolution every 23.93 h and has an equatorial radius of 6380 km.

Accepted Answer

A) 74.0 m/s 
B) 116 m/s 
C) 148 m/s 
D) 232 m/s 
E) 465 m/s

Question 12

The original Ferris wheel had a radius of 38 m and completed a full revolution (2$\pi$radians) every two minutes when operating at its maximum speed. If the wheel were uniformly slowed from its maximum speed to a stop in 35 seconds, what would be the magnitude of the tangential acceleration at the outer rim of the wheel during its deceleration?

Accepted Answer

A) 0.0015 m/s2 
B) 0.057 m/s2 
C) 0.54 m/s2 
D) 1.6 m/s2 
E) 6.8 m/s2

Question 13

A wheel of radius 0.5 m rotates with a constant angular speed about an axis perpendicular to its center. A point on the wheel that is 0.2 m from the center has a tangential speed of 2 m/s.
-Determine the angular speed of the wheel.

Accepted Answer

A) 0.4 rad/s 
B) 2.0 rad/s 
C) 4.0 rad/s 
D) 10 rad/s 
E) 20 rad/s

Question 14

A wheel of radius 0.5 m rotates with a constant angular speed about an axis perpendicular to its center. A point on the wheel that is 0.2 m from the center has a tangential speed of 2 m/s.
-Determine the tangential acceleration of the point that is 0.2 m from the center.

Accepted Answer

A) 0.4 m/s2 
B) 2.0 m/s2 
C) 4.0 m/s2 
D) 10 m/s2 
E) zero m/s2

Question 15

A 2.0-kg solid disk rolls without slipping on a horizontal surface so that its center proceeds to the right with speed 5.0 m/s.  
The point A is the uppermost point on the disk and the point B is along the horizontal line that connects the center of the disk to the rim.
-What is the instantaneous speed of point B with respect to the ground?

Accepted Answer

A) zero m/s 
B) 5.0 m/s 
C) 7.1 m/s 
D) 7.5 m/s 
E) 10.0 m/s

Question 16

A circular hula hoop rolls upright without slipping on a flat horizontal surface. Which one of the following statements is necessarily true?

Accepted Answer

A) All points on the rim of the hoop have the same speed. 
B) All points on the rim of the hoop have the same velocity. 
C) Every point on the rim of the wheel has a different velocity. 
D) All points on the rim of the hoop have acceleration vectors that are tangent to the hoop. 
E) All points on the rim of the hoop have acceleration vectors that point toward the center of the hoop.

Question 17

A 2.0-kg solid disk rolls without slipping on a horizontal surface so that its center proceeds to the right with speed 5.0 m/s.  
The point A is the uppermost point on the disk and the point B is along the horizontal line that connects the center of the disk to the rim.
-What is the instantaneous speed of the point of the disk that makes contact with the surface?

Accepted Answer

A) zero m/s 
B) 5.0 m/s 
C) 7.1 m/s 
D) 7.5 m/s 
E) 10.0 m/s

Question 18

A bicycle wheel of radius 0.70 m is rotating at an angular speed of 6.3 rad/s as it rolls on a horizontal surface without slipping. What is the linear speed of the wheel?

Accepted Answer

A) 1.4 m/s 
B) 28 m/s 
C) 0.11 m/s 
D) 4.4 m/s 
E) 9.1 m/s

Question 19

A bicycle has tires of radius 0.35 meters. If the bicycle is traveling at a constant speed of 7.8 m/s, at approximately what angular speed are the tires rotating?

Accepted Answer

A) 85 rev/min 
B) 197 rev/min 
C) 214 rev/min 
D) 327 rev/min 
E) 423 rev/min

Question 20

A bicycle with wheels of radius 0.4 m travels on a level road at a speed of 8 m/s. What is the angular speed of the wheels?

Accepted Answer

A) 10 rad/s 
B) 20 rad/s 
C) ($\pi$/10)rad/s 
D) (10$\pi$)rad/s 
E) (20/$\pi$)rad/s

Exam 8: Rotational Kinematics

Complete the following statement: The angular measure 1.0 radian is equal to

Which one of the following statements concerning a wheel undergoing rolling motion is true?

Which equation is valid only when the angular measure is expressed in radians?

A bicycle wheel of radius 0.70 m is rolling without slipping on a horizontal surface with an angular speed of 2.0 rev/s when the cyclist begins to uniformly apply the brakes. The bicycle stops in 5.0 s. -Through how many revolutions did the wheel rotate during the 5.0 seconds of braking?

A sculptor is sharpening a chisel on grindstone of radius 1.0 m that is spinning with a constant angular speed of 2.0 rad/s. -What is the magnitude of the centripetal acceleration of a point on the rim of the grindstone?

A grindstone of radius 4.0 m is initially spinning with an angular speed of 8.0 rad/s. The angular speed is then increased to 12 rad/s over the next 4.0 seconds. Assume that the angular acceleration is constant. -Through how many revolutions does the grindstone turn during the 4.0-second interval?

A fan rotating with an initial angular velocity of 1000 rev/min is switched off. In 2 seconds, the angular velocity decreases to 200 rev/min. Assuming the angular acceleration is constant, how many revolutions does the blade undergo during this time?

A sculptor is sharpening a chisel on grindstone of radius 1.0 m that is spinning with a constant angular speed of 2.0 rad/s. -What is the magnitude of the tangential acceleration of a point on the rim of the wheel?

A circular disk of radius 2.0 m rotates, starting from rest, with a constant angular acceleration of 20.0 rad/s². What is the tangential acceleration of a point on the edge of the disk at the instant that its angular speed is 1.0 rev/s?

What is the tangential speed of Nairobi, Kenya, a city near the equator? The earth makes one revolution every 23.93 h and has an equatorial radius of 6380 km.

A wheel of radius 0.5 m rotates with a constant angular speed about an axis perpendicular to its center. A point on the wheel that is 0.2 m from the center has a tangential speed of 2 m/s. -Determine the angular speed of the wheel.

A wheel of radius 0.5 m rotates with a constant angular speed about an axis perpendicular to its center. A point on the wheel that is 0.2 m from the center has a tangential speed of 2 m/s. -Determine the tangential acceleration of the point that is 0.2 m from the center.

A circular hula hoop rolls upright without slipping on a flat horizontal surface. Which one of the following statements is necessarily true?

A bicycle wheel of radius 0.70 m is rotating at an angular speed of 6.3 rad/s as it rolls on a horizontal surface without slipping. What is the linear speed of the wheel?

A bicycle has tires of radius 0.35 meters. If the bicycle is traveling at a constant speed of 7.8 m/s, at approximately what angular speed are the tires rotating?

A bicycle with wheels of radius 0.4 m travels on a level road at a speed of 8 m/s. What is the angular speed of the wheels?