Question 1

A 1.0-g bead is at (-2.0 cm, 2.0 cm), a 2.0-g bead is at (2.0 cm, -4.0 cm), and a 3.0-g bead is at (2.0 cm, 0.0 cm). What are the coordinates of the center of mass (or center of gravity) of this system of beads?

Accepted Answer

The answer of A 1.0-g bead is at (-2.0 cm,...

Question 2

The rotating systems shown in the figure differ only in that the two identical movable masses are positioned a distance r from the axis of rotation (left), or a distance r/2 from the axis of rotation (right). If you release the hanging blocks simultaneously from rest,

Accepted Answer

A)  the block at the left lands first. 
B)  the block at the right lands first. 
C)  both blocks land at the same time.

Question 3

A pulley has an initial angular speed of 12.5 rad/s and a constant angular acceleration of 3.41 rad/s2. Through what angle does the pulley turn in 5.26 s?

Accepted Answer

A)  113 rad 
B)  22.6 rad 
C)  42.6 rad 
D)  19.3 rad 
E)  160 rad

Question 4

A 2.0-m rope is lying on a table. You pick up one end and start raising it vertically. How high above the table is the center of mass (or center of gravity) of the rope when half of the rope has lifted off the table?

Accepted Answer

A)  0.25 m 
B)  0.50 m 
C)  0.75 m 
D)  1.0 m 
E)  1.5 m

Question 5

A wheel accelerates with a constant angular acceleration of 4.5 rad/s² from an initial angular speed of 1.0 rad/s. (a) Through what angle does the wheel turn in the first 2.0 s, and (b) what is its angular speed at that time?

Accepted Answer

The answer of A wheel accelerates with a constant angular...

Question 6

When an old LP turntable was revolving at 33 $\frac { 1 } { 3 }$ rpm, it was shut off and uniformly slowed down and stopped in 5.5 seconds. (a) What was the magnitude of its angular acceleration (in rad/s²) as it slowed down? (b) Through how many revolutions did it turn while stopping?

Accepted Answer

The answer of When an old LP turntable was revolving...

Question 7

A car is traveling along a freeway at 65 mph. What is the linear speed, relative to the highway, of each of the following points on one of its tires?
(a) the highest point on the tire
(b) the lowest point on a tire
(c) the center of the tire

Accepted Answer

The answer of A car is traveling along a freeway...

Question 8

A 375-g stone hangs from a thin light string that is wrapped around the circumference of a frictionless pulley with a moment of inertia of 0.0125 kg ∙ m² and a radius of 26 cm. When the stone is released, the stone accelerates downward and the pulley rotates about its axis as the string unwinds. (a) What is the magnitude of the acceleration of the stone? (b) What is the tension in the string?

Accepted Answer

The answer of A 375-g stone hangs from a thin...

Question 9

A 385-g tile hangs from one end of a string that goes over a pulley with a moment of inertia of $0.0125 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$ and a radius of 15.0 cm. A mass of 710 g hangs from the other end of the string. When the tiles are released, the larger one accelerates downward while the lighter one accelerates upward. The pulley has no friction in its axle and turns without the string slipping. What is the tension in the string on the side of the 710-g tile?

Accepted Answer

A)  9.77 N 
B)  6.87 N 
C)  5.59 N 
D)  4.41 N 
E)  3.68 N

Question 10

An old LP record that is originally rotating at 33.3 rad/s is given a uniform angular acceleration of 2.15 rad/s2. Through what angle has the record turned when its angular speed reaches 72.0 rad/s?

Accepted Answer

A)  83.2 rad 
B)  316 rad 
C)  697 rad 
D)  66.8 rad 
E)  948 rad

Question 11

A mechanic is examining the wheel of a bicycle to adjust the brake. With the bicycle off the ground, he manually rotates the wheel until it reaches an angular speed of 12.0 rad/s and then allows it to coast to a stop. If the wheel has a moment of inertia of 0.100 kg ∙ m2, and the wheel slows uniformly to a stop in 160 s, what is the magnitude of the retarding torque?

Accepted Answer

A)  1.00 N ∙ m 
B)  0.00750 N ∙ m 
C)  0.0787 N ∙ m 
D)  1.33 N ∙ m 
E)  1.67 N ∙ m

Question 12

Five forces act on a rod that is free to pivot at point P, as shown in the figure. Which of these forces is producing a counter-clockwise torque about point P? (There could be more than one correct choice.)

Accepted Answer

A)  force A 
B)  force B 
C)  force C 
D)  force D 
E)  force E

Question 13

A bicycle has wheels that are 60 cm in diameter. What is the angular speed of these wheels when it is moving at 4.0 m/s?

Accepted Answer

A)  1.2 rad/s 
B)  4.8 rad/s 
C)  0.36 rad/s 
D)  13 rad/s 
E)  7.6 rad/s

Question 14

A uniform solid cylinder of mass 10 kg can rotate about a frictionless axle through its center O, as shown in the cross-sectional view in the figure. A rope wrapped around the outer radius R1 = 1.0 m exerts a force of magnitude F1 = 5.0 N to the right. A second rope wrapped around another section of radius R2 = 0.50 m exerts a force of magnitude F2 = 6.0 N downward. How many radians does the cylinder rotate through in the first 5.0 seconds, if it starts from rest?

Accepted Answer

A)  13 rad 
B)  7.5 rad 
C)  5.0 rad 
D)  10 rad

Question 15

A uniform solid cylinder of mass 10 kg can rotate about a frictionless axle through its center O, as shown in the cross-sectional view in the figure. A rope wrapped around the outer radius R1 = 1.0 m exerts a force of magnitude F1 = 5.0 N to the right. A second rope wrapped around another section of radius R2 = 0.50 m exerts a force of magnitude F2 = 6.0 N downward. What is the angular acceleration of the cylinder?

Accepted Answer

A)  1.0 rad/s2 
B)  0.60 rad/s2 
C)  0.40 rad/s2 
D)  0.80 rad/s2

Exam 7: Rotational Motion

A 1.0-g bead is at (-2.0 cm, 2.0 cm), a 2.0-g bead is at (2.0 cm, -4.0 cm), and a 3.0-g bead is at (2.0 cm, 0.0 cm). What are the coordinates of the center of mass (or center of gravity) of this system of beads?

The rotating systems shown in the figure differ only in that the two identical movable masses are positioned a distance r from the axis of rotation (left) , or a distance r/2 from the axis of rotation (right) . If you release the hanging blocks simultaneously from rest,

A pulley has an initial angular speed of 12.5 rad/s and a constant angular acceleration of 3.41 rad/s². Through what angle does the pulley turn in 5.26 s?

A 2.0-m rope is lying on a table. You pick up one end and start raising it vertically. How high above the table is the center of mass (or center of gravity) of the rope when half of the rope has lifted off the table?

A wheel accelerates with a constant angular acceleration of 4.5 rad/s² from an initial angular speed of 1.0 rad/s. (a) Through what angle does the wheel turn in the first 2.0 s, and (b) what is its angular speed at that time?

When an old LP turntable was revolving at 33 $\frac { 1 } { 3 }$ rpm, it was shut off and uniformly slowed down and stopped in 5.5 seconds. (a) What was the magnitude of its angular acceleration (in rad/s²) as it slowed down? (b) Through how many revolutions did it turn while stopping?

A car is traveling along a freeway at 65 mph. What is the linear speed, relative to the highway, of each of the following points on one of its tires? (a) the highest point on the tire (b) the lowest point on a tire (c) the center of the tire

An old LP record that is originally rotating at 33.3 rad/s is given a uniform angular acceleration of 2.15 rad/s². Through what angle has the record turned when its angular speed reaches 72.0 rad/s?

Five forces act on a rod that is free to pivot at point P, as shown in the figure. Which of these forces is producing a counter-clockwise torque about point P? (There could be more than one correct choice.)

A bicycle has wheels that are 60 cm in diameter. What is the angular speed of these wheels when it is moving at 4.0 m/s?

Exam 7: Rotational Motion

A 1.0-g bead is at (-2.0 cm, 2.0 cm), a 2.0-g bead is at (2.0 cm, -4.0 cm), and a 3.0-g bead is at (2.0 cm, 0.0 cm). What are the coordinates of the center of mass (or center of gravity) of this system of beads?

The rotating systems shown in the figure differ only in that the two identical movable masses are positioned a distance r from the axis of rotation (left) , or a distance r/2 from the axis of rotation (right) . If you release the hanging blocks simultaneously from rest,

A pulley has an initial angular speed of 12.5 rad/s and a constant angular acceleration of 3.41 rad/s2. Through what angle does the pulley turn in 5.26 s?

A 2.0-m rope is lying on a table. You pick up one end and start raising it vertically. How high above the table is the center of mass (or center of gravity) of the rope when half of the rope has lifted off the table?

A wheel accelerates with a constant angular acceleration of 4.5 rad/s2 from an initial angular speed of 1.0 rad/s. (a) Through what angle does the wheel turn in the first 2.0 s, and (b) what is its angular speed at that time?

When an old LP turntable was revolving at 33 13\frac { 1 } { 3 }31​ rpm, it was shut off and uniformly slowed down and stopped in 5.5 seconds. (a) What was the magnitude of its angular acceleration (in rad/s2) as it slowed down? (b) Through how many revolutions did it turn while stopping?

A car is traveling along a freeway at 65 mph. What is the linear speed, relative to the highway, of each of the following points on one of its tires? (a) the highest point on the tire (b) the lowest point on a tire (c) the center of the tire

An old LP record that is originally rotating at 33.3 rad/s is given a uniform angular acceleration of 2.15 rad/s2. Through what angle has the record turned when its angular speed reaches 72.0 rad/s?

Five forces act on a rod that is free to pivot at point P, as shown in the figure. Which of these forces is producing a counter-clockwise torque about point P? (There could be more than one correct choice.)

A bicycle has wheels that are 60 cm in diameter. What is the angular speed of these wheels when it is moving at 4.0 m/s?

A pulley has an initial angular speed of 12.5 rad/s and a constant angular acceleration of 3.41 rad/s². Through what angle does the pulley turn in 5.26 s?

A wheel accelerates with a constant angular acceleration of 4.5 rad/s² from an initial angular speed of 1.0 rad/s. (a) Through what angle does the wheel turn in the first 2.0 s, and (b) what is its angular speed at that time?

When an old LP turntable was revolving at 33 $\frac { 1 } { 3 }$ rpm, it was shut off and uniformly slowed down and stopped in 5.5 seconds. (a) What was the magnitude of its angular acceleration (in rad/s²) as it slowed down? (b) Through how many revolutions did it turn while stopping?

An old LP record that is originally rotating at 33.3 rad/s is given a uniform angular acceleration of 2.15 rad/s². Through what angle has the record turned when its angular speed reaches 72.0 rad/s?