Question 1

A wheel accelerates from rest to  59 rad/s at a uniform rate of $58 \mathrm { rad } / \mathrm { s } ^ { 2 }$ Through what angle (in radians) did the wheel turn while accelerating?

Accepted Answer

A)   30 rad 
B)   60 rad 
C)   38 rad 
D)   24 rad

Question 2

A machinist turns on the power on to a grinding wheel at time  t=0 s. The wheel accelerates uniformly from rest for  10 s and reaches the operating angular speed of  96 rad/s. The wheel is  run  at that angular velocity for  40 s and then power is shut off. The wheel slows down uniformly at $1.5 \mathrm { rad } / \mathrm { s } ^ { 2 }$ until the wheel stops. For how long a time after the power is shut off does it take the wheel to stop?

Accepted Answer

A)   68 s 
B)   64 s 
C)   62 s 
D)   66 s 
E)   70 s

Question 3

A small  355-g box hangs from one end of a thin light string that goes over a frictionless pulley having a moment of inertia of  0.0125  $k g \cdot m ^ { 2 }$ and a radius of  15 cm. A second small package, this one of mass  680 g, hangs from the other end of the string. When the packages are released, the larger one accelerates downward, the lighter one accelerates upward, and the pulley turns without the string slipping.
(a) What is the tension in the string on the side of the  355-g  package?
(b) At what rate do the packages change their speeds?

Accepted Answer

The answer of A small  355-g box hangs from...

Question 4

A machinist turns on the power to a grinding wheel at time  t=0 s. The wheel accelerates
uniformly from rest for  10 s and reaches the operating angular speed of  38 rad/s . The wheel is run
at that angular speed for  30 s and then power is shut off. The wheel slows down uniformly at
$2.1 \mathrm { rad } / \mathrm { s } ^ { 2 }$
between  t=0 s and  t=10 s ?

Accepted Answer

A)  $6.1 \mathrm { rad } / \mathrm { s } ^ { 2 }$ 
B)  $5.3 \mathrm { rad } / \mathrm { s } ^ { 2 }$ 
C)  $6.8 \mathrm { rad } / \mathrm { s } ^ { 2 }$ 
D)  $3.8 \mathrm { rad } / \mathrm { s } ^ { 2 }$ 
E)  $4.6 \mathrm { rad } / \mathrm { s } ^ { 2 }$

Question 5

A hoop is rolling without slipping along a horizontal surface with a forward speed of 5.50 m/s when it starts up a ramp that makes an angle of $25.0 ^ { \circ }$ with the horizontal. What is the speed of the
Hoop after it has rolled 3.00 m up as measured along the surface of the ramp?

Accepted Answer

A)  1.91 m/s 
B)  4.22 m/s 
C)  3.79 m/s 
D)  8.02 m/s 
E)  2.06 m/s

Question 6

Two uniform solid balls, one of radius R and mass M, the other of radius 2R and mass 8M, roll down a high incline. They start together from rest at the top of the incline. Which one will reach the
Bottom of the incline first?

Accepted Answer

A)  The large sphere arrives first. 
B)  The small sphere arrives first. 
C)  Both reach the bottom at the same time.

Question 7

The sun subtends an angle of  0.00928  rad when viewed from the surface of the earth, and its distance from Earth is $1.5 \times 10 ^ { 11 } \mathrm {~m}$
What is the diameter of the sun?

Accepted Answer

The answer of The sun subtends an angle of ...

Question 8

An old  78 rpm record rotates through an angle of $320 ^ { \circ }$ as it slows down uniformly from  78.0 rpm  to  22.8 rpm. What is the magnitude of the angular acceleration of the record?

Accepted Answer

A)  $5.46 \mathrm { rad } / \mathrm { s } ^ { 2 }$ 
B)  $2.34 \mathrm { rad } / \mathrm { s } ^ { 2 }$ 
C)  $10.9 \mathrm { rad } / \mathrm { s } 2$ 
D)  $8.35 \mathrm { rad } / \mathrm { s } ^ { 2 }$ 
E)  $6.50 \mathrm { rad } / \mathrm { s } ^ { 2 }$

Question 9

A Ferris wheel rotating at  20 rad/s slows down with a constant angular acceleration of magnitude $5.0 \mathrm { rad } / \mathrm { s } ^ { 2 }$
How many revolutions does it make while slowing down before coming to rest?

Accepted Answer

A)   3.2 
B)  20 
C)  40 
D)   6.4

Question 10

A merry-go-round spins freely when Diego moves quickly to the center along a radius of the merry-go-round. As he does this, it is true to say that

Accepted Answer

A)  the moment of inertia of the system decreases and the angular speed decreases. 
B)  the moment of inertia of the system decreases and the angular speed remains the same. 
C)  the moment of inertia of the system decreases and the angular speed increases. 
D)  the moment of inertia of the system increases and the angular speed increases. 
E)  the moment of inertia of the system increases and the angular speed decreases.

Question 11

A wheel of diameter 0.70 m rolls on the floor without slipping. A point at the top of the
wheel moves with a speed 2.0 m/s relative to the floor.
(a) At what speed is the central axis of the wheel moving relative to the floor?
(b) What is the angular speed of the wheel?

Accepted Answer

The answer of A wheel of diameter 0.70 m rolls...

Question 12

A string is wound tightly around a fixed pulley having a radius of 5.0 cm. As the string is pulled, the pulley rotates without any slipping of the string. What is the angular speed of the pulley when
The string is moving at 5.0 m/s?

Accepted Answer

A)  50 rad/s 
B)  10 rad/s 
C)  25 rad/s 
D)  100 rad/s 
E)  20 rad/s

Question 13

A wheel accelerates with a constant angular acceleration of $4.5 \mathrm { rad } / \mathrm { s } ^ { 2 }$ 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 anqular speed at that time?

Accepted Answer

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

Question 14

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)  7.6 rad/s 
C)  13 rad/s 
D)  0.36 rad/s 
E)  4.8 rad/s

Question 15

When a fan is turned off, its angular speed decreases from 10 rad/s to 6.3 rad/s in 5.0 s. What is the magnitude of the average angular acceleration of the fan?

Accepted Answer

A)  $0,74 \mathrm { rad } / \mathrm { s } ^ { 2 }$ 
B)  $1.2 \mathrm { rad } / \mathrm { s } ^ { 2 }$ 
C)  $11 \mathrm { rad } / \mathrm { s } ^ { 2 }$ 
D)  $0.37 \mathrm { rad } / \mathrm { s } ^ { 2 }$ 
E)  $0.86 \mathrm { rad } / \mathrm { s } 2$

Question 16

Three solid, uniform, cylindrical flywheels, each of mass  65.0 kg and radius  1.47 m, rotate independently around a common axis through their centers. Two of the flywheels rotate in one direction at  8.94 rad/s, but the other one rotates in the opposite direction at  3.42 rad/s. Calculate the magnitude of the net angular momentum of the system.

Accepted Answer

A)  $1020 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$ 
B)  $975 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$ 
C)  $940 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$ 
D)  $1500 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$

Question 17

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 18

A  40.0-kg child running at  3.00 m/s suddenly jumps onto a stationary playground merry-go-round at a distance  1.50 m from the axis of rotation of the merry-go-round. The child is traveling tangential to the edge of the merry-go-round just before jumping on. The moment of inertia about its axis of rotation is $600 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$ and very little friction at its rotation axis. What is the angular speed of the merry-go-round just after the child has jumped onto it?

Accepted Answer

A)   0.261 rad/s 
B)   3.14 rev/s 
C)   2.00 rad/s 
D)   6.28 rev/s 
E)   0.788 rad/s

Question 19

A solid uniform sphere of mass  120 kg and radius  1.7 m  starts from rest and rolls without slipping down an inclined plane of vertical height  5.3 m. What is the angular speed of the sphere at the bottom of the inclined plane?

Accepted Answer

A)   8.7 rad/s 
B)   9.7 rad/s 
C)   5.1 rad/s 
D)   6.1 rad/s

Question 20

As shown in the figure, a  35.30-kg box is attached to a light string that is wrapped around a cylindrical frictionless spool of radius  10.0 cm and moment of inertia $4.00 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$
The spool is suspended from the ceiling, and the box is then released from rest a distance  3.50 m above the floor. How long does it take for the box to reach the floor?

Accepted Answer

A)   2.97 s 
B)   2.85 s 
C)   4.18 s 
D)   5.89 s 
E)   0.892 s

Exam 8: Rotational Motion

A wheel accelerates from rest to 59 rad/s at a uniform rate of 58rad/s258 \mathrm { rad } / \mathrm { s } ^ { 2 }58rad/s2 Through what angle (in radians) did the wheel turn while accelerating?

A hoop is rolling without slipping along a horizontal surface with a forward speed of 5.50 m/s when it starts up a ramp that makes an angle of 25.0∘25.0 ^ { \circ }25.0∘ with the horizontal. What is the speed of the Hoop after it has rolled 3.00 m up as measured along the surface of the ramp?

Two uniform solid balls, one of radius R and mass M, the other of radius 2R and mass 8M, roll down a high incline. They start together from rest at the top of the incline. Which one will reach the Bottom of the incline first?

The sun subtends an angle of 0.00928 rad when viewed from the surface of the earth, and its distance from Earth is 1.5×1011 m1.5 \times 10 ^ { 11 } \mathrm {~m}1.5×1011 m What is the diameter of the sun?

An old 78 rpm record rotates through an angle of 320∘320 ^ { \circ }320∘ as it slows down uniformly from 78.0 rpm to 22.8 rpm. What is the magnitude of the angular acceleration of the record?

A Ferris wheel rotating at 20 rad/s slows down with a constant angular acceleration of magnitude 5.0rad/s25.0 \mathrm { rad } / \mathrm { s } ^ { 2 }5.0rad/s2 How many revolutions does it make while slowing down before coming to rest?

A merry-go-round spins freely when Diego moves quickly to the center along a radius of the merry-go-round. As he does this, it is true to say that

A wheel of diameter 0.70 m rolls on the floor without slipping. A point at the top of the wheel moves with a speed 2.0 m/s relative to the floor. (a) At what speed is the central axis of the wheel moving relative to the floor? (b) What is the angular speed of the wheel?

A string is wound tightly around a fixed pulley having a radius of 5.0 cm. As the string is pulled, the pulley rotates without any slipping of the string. What is the angular speed of the pulley when The string is moving at 5.0 m/s?

A wheel accelerates with a constant angular acceleration of 4.5rad/s24.5 \mathrm { rad } / \mathrm { s } ^ { 2 }4.5rad/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 anqular speed at that time?

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?

When a fan is turned off, its angular speed decreases from 10 rad/s to 6.3 rad/s in 5.0 s. What is the magnitude of the average angular acceleration of the fan?

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

A solid uniform sphere of mass 120 kg and radius 1.7 m starts from rest and rolls without slipping down an inclined plane of vertical height 5.3 m. What is the angular speed of the sphere at the bottom of the inclined plane?

A wheel accelerates from rest to 59 rad/s at a uniform rate of $58 \mathrm { rad } / \mathrm { s } ^ { 2 }$ Through what angle (in radians) did the wheel turn while accelerating?

A hoop is rolling without slipping along a horizontal surface with a forward speed of 5.50 m/s when it starts up a ramp that makes an angle of $25.0 ^ { \circ }$ with the horizontal. What is the speed of the Hoop after it has rolled 3.00 m up as measured along the surface of the ramp?

The sun subtends an angle of 0.00928 rad when viewed from the surface of the earth, and its distance from Earth is $1.5 \times 10 ^ { 11 } \mathrm {~m}$ What is the diameter of the sun?

An old 78 rpm record rotates through an angle of $320 ^ { \circ }$ as it slows down uniformly from 78.0 rpm to 22.8 rpm. What is the magnitude of the angular acceleration of the record?

A Ferris wheel rotating at 20 rad/s slows down with a constant angular acceleration of magnitude $5.0 \mathrm { rad } / \mathrm { s } ^ { 2 }$ How many revolutions does it make while slowing down before coming to rest?

A wheel accelerates with a constant angular acceleration of $4.5 \mathrm { rad } / \mathrm { s } ^ { 2 }$ 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 anqular speed at that time?