Question 1

A grinding wheel has a mass of $250 \mathrm{~kg}$ and moment of inertia of $500 \mathrm{~kg} \mathrm{~m}^{2}$. A torque of $100 \mathrm{~N} \cdot \mathrm{m}$ is applied to the grinding wheel. If the wheel starts from rest, what is the angular momentum of the wheel after 5.0 seconds?

Accepted Answer

A)  $650 \mathrm{~kg} \mathrm{~m}^{2} / \mathrm{s}$ 
B)  $500 \mathrm{~kg} \mathrm{~m}^{2} / \mathrm{s}$ 
C)  $250 \mathrm{~kg} \mathrm{~m}^{2} / \mathrm{s}$ 
D)  $450 \mathrm{~kg} \mathrm{~m}^{2} / \mathrm{s}$ 
E)  $300 \mathrm{~kg} \mathrm{~m}^{2} / \mathrm{s}$

Question 2

A mass $m_{1}$ is connected by a light string that passes over a pulley of mass $M$ to a mass $m_{2}$ sliding on a frictionless horizontal surface as shown in the figure. There is no slippage between the string and the pulley. The pulley has a radius of $25.0 \mathrm{~cm}$ and a moment of inertia of $1 / 2 \mathrm{MR}^{2}$. If $\mathrm{m}_{1}$ is $1.00 \mathrm{~kg}, \mathrm{~m}_{2}$ is $2.00 \mathrm{~kg}$, and M is $4.00 \mathrm{~kg}$, then what is the downward acceleration of $m_{1}$ ?

Accepted Answer

A)  $2.72 \mathrm{~m} / \mathrm{s}^{2}$ 
B)  $1.55 \mathrm{~m} / \mathrm{s}^{2}$ 
C)  $1.96 \mathrm{~m} / \mathrm{s}^{2}$ 
D)  $2.06 \mathrm{~m} / \mathrm{s}^{2}$ 
E)  $2.33 \mathrm{~m} / \mathrm{s}^{2}$

Question 3

A torque of $15.0 \mathrm{~N} \cdot \mathrm{m}$ is applied to a bolt. The bolt rotates through an angle of 360 degrees. The work done in turning the bolt is

Accepted Answer

A)  $96.7 \mathrm{~J}$. 
B)  $91.3 \mathrm{~J}$. 
C)  $98.1 \mathrm{~J}$. 
D)  $89.9 \mathrm{~J}$. 
E)  $94.2 \mathrm{~J}$.

Question 4

A $75.0 \mathrm{~kg}$ ladder that is $3.00 \mathrm{~m}$ long is placed against a wall at an angle theta. The center of gravity of the ladder is at a point $1.20 \mathrm{~m}$ from the base of the ladder. The coefficient of static friction at the base of the ladder is 0.800 . There is no friction between the wall and the ladder. What is the vertical force of the ground on the ladder?

Accepted Answer

A)  $735 \mathrm{~N}$ 
B)  $832 \mathrm{~N}$ 
C)  $625 \mathrm{~N}$ 
D)  $900 \mathrm{~N}$ 
E)  $640 \mathrm{~N}$

Question 5

What is the rotational inertia of a solid iron disk of mass $41.0 \mathrm{~kg}$ with a thickness of $5.00 \mathrm{~cm}$ and radius of $30.0 \mathrm{~cm}$, about an axis perpendicular to the disk and passing through its center?

Accepted Answer

A)  $0.980 \mathrm{~kg} \mathrm{~m}^{2}$ 
B)  $0.761 \mathrm{~kg} \mathrm{~m}^{2}$ 
C)  $2.29 \mathrm{~kg} \mathrm{~m}^{2}$ 
D)  $1.85 \mathrm{~kg} \mathrm{~m}^{2}$

Question 6

A mass $m_{1}$ is connected by a light string that passes over a pulley of mass $M$ to a mass $m_{2}$ sliding on a frictionless horizontal surface as shown in the figure. There is no slippage between the string and the pulley. The pulley has a radius of $25 \mathrm{~cm}$ and a moment of inertia of $1 / 2 \mathrm{MR}^{2}$. If $\mathrm{m}_{1}$ is $4.00 \mathrm{~kg}, \mathrm{~m}_{2}$ is $2.00 \mathrm{~kg}$, and $\mathrm{M}$ is $4.00 \mathrm{~kg}$, then what is the downward acceleration of $\mathrm{m}_{1}$ ?

Accepted Answer

A)  $4.9 \mathrm{~m} / \mathrm{s}^{2}$ 
B)  $4.5 \mathrm{~m} / \mathrm{s}^{2}$ 
C)  $3.7 \mathrm{~m} / \mathrm{s}^{2}$ 
D)  $4.1 \mathrm{~m} / \mathrm{s}^{2}$ 
E)  $3.9 \mathrm{~m} / \mathrm{s}^{2}$

Question 7

A mass $m_{1}$ is connected by a light string that passes over a pulley of mass $M$ to a mass $m_{2}$ sliding on a frictionless horizontal surface as shown in the figure. There is no slippage between the string and the pulley. The pulley has a radius of $25.0 \mathrm{~cm}$ and a moment of inertia of $1 / 2 \mathrm{MR}^{2}$. If $\mathrm{m}_{1}$ is $4.00 \mathrm{~kg}, \mathrm{~m}_{2}$ is $4.00 \mathrm{~kg}$, and M is $4.00 \mathrm{~kg}$, then what is the tension in the string attached to $\mathrm{m}_{2}$ ?

Accepted Answer

A)  $12.6 \mathrm{~N}$ 
B)  $15.7 \mathrm{~N}$ 
C)  $19.8 \mathrm{~N}$ 
D)  $10.4 \mathrm{~N}$ 
E)  $17.6 \mathrm{~N}$

Question 8

A $4.00 \mathrm{~kg}$ hollow sphere $\left(\mathrm{I}=2 / 3 \mathrm{MR}^{2}\right)$ is spinning with an angular velocity of $10.0 \mathrm{rad} / \mathrm{s}$. The diameter of the sphere is $20.0 \mathrm{~cm}$. The rotational kinetic energy of the spinning sphere is

Accepted Answer

A)  $1.50 \mathrm{~J}$. 
B)  $0.90 \mathrm{~J}$. 
C)  $1.75 \mathrm{~J}$. 
D)  $1.33 \mathrm{~J}$. 
E)  $0.75 \mathrm{~J}$.

Question 9

A person rides a bicycle along a straight road. From the point of view of the rider, what's the direction of the angular momentum vector of the front wheel?

Accepted Answer

A)  left 
B)  up 
C)  down 
D)  backward 
E)  forward
F) right

Question 10

The rotational inertia of a thin rod about one end is $1 / 3 \mathrm{ML}^{2}$. What is the rotational inertia of the same rod about a point located $0.40 \mathrm{~L}$ from the end?

Accepted Answer

A)  $0.093 \mathrm{ML}^{2}$ 
B)  $0.493 \mathrm{ML}^{2}$ 
C)  $0.073 \mathrm{ML}^{2}$ 
D)  $0.243 \mathrm{ML}^{2}$ 
E)  $0.056 \mathrm{ML}^{2}$

Question 11

An $8.00 \mathrm{~kg}$ object has a moment of inertia of $1.50 \mathrm{~kg} \mathrm{~m}^{2}$. If a torque of $2.00 \mathrm{~N} \cdot \mathrm{m}$ is applied to the object, the angular acceleration is

Accepted Answer

A)  $1.33 \mathrm{rad} / \mathrm{s}^{2}$. 
B)  $1.00 \mathrm{rad} / \mathrm{s}^{2}$. 
C)  $2.01 \mathrm{rad} / \mathrm{s}^{2}$. 
D)  $0.750 \mathrm{rad} / \mathrm{s}^{2}$. 
E)  $2.67 \mathrm{rad} / \mathrm{s}^{2}$.

Question 12

A $4.00 \mathrm{~kg}$ hollow cylinder of radius $5.00 \mathrm{~cm}$ starts from rest and rolls without slipping down a 30.0 degree incline. If the length of the incline is $50.0 \mathrm{~cm}$, then the velocity of the center of mass of the cylinder at the bottom of the incline is

Accepted Answer

A)  $3.02 \mathrm{~m} / \mathrm{s}$. 
B)  $1.35 \mathrm{~m} / \mathrm{s}$. 
C)  $2.55 \mathrm{~m} / \mathrm{s}$. 
D)  $1.82 \mathrm{~m} / \mathrm{s}$. 
E)  $1.57 \mathrm{~m} / \mathrm{s}$

Question 13

A $10 \mathrm{~kg}$ sphere with a $25.0 \mathrm{~cm}$ radius has a moment of inertia of $2 / 5 \mathrm{MR} 2$. If a torque of $2.0 \mathrm{~N} \cdot \mathrm{m}$ is applied to the object, the angular acceleration is

Accepted Answer

A)  $2.0 \mathrm{rad} / \mathrm{s}^{2}$. 
B)  $4.0 \mathrm{rad} / \mathrm{s}^{2}$. 
C)  $8.0 \mathrm{rad} / \mathrm{s}^{2}$. 
D)  $1.0 \mathrm{rad} / \mathrm{s}^{2}$. 
E)  $6.0 \mathrm{rad} / \mathrm{s}^{2}$.

Question 14

A mass $m_{1}$ is connected by a light string that passes over a pulley of mass $M$ to a mass $m_{2}$ sliding on a frictionless horizontal surface as shown in the figure. There is no slippage between the string and the pulley. The pulley has a radius of $25.0 \mathrm{~cm}$ and a moment of inertia of $1 / 2 \mathrm{MR}^{2}$. If $\mathrm{m}_{1}$ is $4.00 \mathrm{~kg}, \mathrm{~m}_{2}$ is $4.00 \mathrm{~kg}$, and M is $4.00 \mathrm{~kg}$, then what is the tension in the string attached to $\mathrm{m}_{1}$ ?

Accepted Answer

A)  $32.7 \mathrm{~N}$ 
B)  $31.0 \mathrm{~N}$ 
C)  $29.0 \mathrm{~N}$ 
D)  $23.5 \mathrm{~N}$ 
E)  $35.6 \mathrm{~N}$

Question 15

A $1.500 \mathrm{~m}$ long uniform beam of mass $30.00 \mathrm{~kg}$ is supported by a wire as shown in the figure. The beam makes an angle of 10.00 degrees with the horizontal and the wire makes an angle of 30.00 degrees with the beam. A $50.00 \mathrm{~kg}$ mass, $\mathrm{m}$, is attached to the end of the beam. What is the tension in the wire?

Accepted Answer

A)  $1,855 \mathrm{~N}$ 
B)  $1,255 \mathrm{~N}$ 
C)  $1,435 \mathrm{~N}$ 
D)  $2,034 \mathrm{~N}$ 
E)  $1,035 \mathrm{~N}$

Question 16

A $6.00 \mathrm{~kg}$ mass is located at $(2.00 \mathrm{~m}, 2.00 \mathrm{~m}, 2.00 \mathrm{~m})$ and a $5.00 \mathrm{~kg}$ mass is located at $(-1.0 \mathrm{~m}, 3.00 \mathrm{~m}$, $-2.00 \mathrm{~m}$ ). The rotational inertia of this system of masses about the Z-axis, perpendicular to the $\mathrm{X}-\mathrm{Y}$ plane, is

Accepted Answer

A)  $98 \mathrm{~kg} \mathrm{~m}^{2}$. 
B)  $79 \mathrm{~kg} \mathrm{~m}^{2}$. 
C)  $60 \mathrm{~kg} \mathrm{~m}^{2}$. 
D)  $112 \mathrm{~kg} \mathrm{~m}^{2}$. 
E)  $85 \mathrm{~kg} \mathrm{~m}^{2}$.

Question 17

A torque of $2.00 \mathrm{~N} \cdot \mathrm{m}$ is applied to a $10.0 \mathrm{~kg}$ object to give it an angular acceleration. If the angular acceleration is $1.75 \mathrm{rad} / \mathrm{s}^{2}$, then the moment of inertia is

Accepted Answer

A)  $1.35 \mathrm{~kg} \mathrm{~m}^{2}$. 
B)  $1.05 \mathrm{~kg} \mathrm{~m}^{2}$. 
C)  $1.20 \mathrm{~kg} \mathrm{~m}^{2}$. 
D)  $1.14 \mathrm{~kg} \mathrm{~m}^{2}$. 
E)  $1.95 \mathrm{~kg} \mathrm{~m}^{2}$.

Question 18

A mass $m_{1}$ is connected by a light string that passes over a pulley of mass $M$ to a mass $m_{2}$ as shown in the figure. Both masses move vertically and there is no slippage between the string and the pulley. The pulley has a radius of $20.0 \mathrm{~cm}$ and a moment of inertia of $1 / 2 \mathrm{MR}^{2}$. If $\mathrm{m}_{1}$ is $3.00 \mathrm{~kg}, \mathrm{~m}_{2}$ is $6.00 \mathrm{~kg}$ and $\mathrm{M}$ is $4.00 \mathrm{~kg}$, then what is the tension in the string that is attached to mass $\mathrm{m}_{1}$ ?

Accepted Answer

A)  $27.4 \mathrm{~N}$ 
B)  $37.4 \mathrm{~N}$ 
C)  $30.2 \mathrm{~N}$ 
D)  $43.5 \mathrm{~N}$ 
E)  $20.8 \mathrm{~N}$

Question 19

A $4.00 \mathrm{~kg}$ mass is located at $(2.00 \mathrm{~m}, 2.00 \mathrm{~m}, 0.00 \mathrm{~m})$ and a $3.00 \mathrm{~kg}$ mass is located at $(-1.0 \mathrm{~m}, 3.00$ $\mathrm{m}, 0.00 \mathrm{~m}$ ). The rotational inertia of this system of masses about the X-axis, perpendicular to the Z-Y plane, is

Accepted Answer

A)  $24 \mathrm{~kg} \mathrm{~m}^{2}$. 
B)  $56 \mathrm{~kg} \mathrm{~m}^{2}$. 
C)  $62 \mathrm{~kg} \mathrm{~m}^{2}$. 
D)  $43 \mathrm{~kg} \mathrm{~m}^{2}$. 
E)  $36 \mathrm{~kg} \mathrm{~m}^{2}$.

Question 20

A $2.00 \mathrm{~kg}$ mass is located at $(4.00 \mathrm{~m}, 0.00 \mathrm{~m}, 0.00 \mathrm{~m})$ and a $4.00 \mathrm{~kg}$ mass is located at $(0.00 \mathrm{~m}, 3.00 \mathrm{~m}$, $0.00 \mathrm{~m}$ ). The rotational inertia of this system of masses about the $\mathrm{X}$-axis, perpendicular to the Z-Y plane, is

Accepted Answer

A)  $28 \mathrm{~kg} \mathrm{~m}^{2}$. 
B)  $36 \mathrm{~kg} \mathrm{~m}^{2}$. 
C)  $33 \mathrm{~kg} \mathrm{~m}^{2}$. 
D)  $23 \mathrm{~kg} \mathrm{~m}^{2}$. 
E)  $41 \mathrm{~kg} \mathrm{~m}^{2}$.

Exam 8: Torque and Angular Momentum

A grinding wheel has a mass of $250 \mathrm{~kg}$ and moment of inertia of $500 \mathrm{~kg} \mathrm{~m}^{2}$ . A torque of $100 \mathrm{~N} \cdot \mathrm{m}$ is applied to the grinding wheel. If the wheel starts from rest, what is the angular momentum of the wheel after 5.0 seconds?

A torque of $15.0 \mathrm{~N} \cdot \mathrm{m}$ is applied to a bolt. The bolt rotates through an angle of 360 degrees. The work done in turning the bolt is

What is the rotational inertia of a solid iron disk of mass $41.0 \mathrm{~kg}$ with a thickness of $5.00 \mathrm{~cm}$ and radius of $30.0 \mathrm{~cm}$ , about an axis perpendicular to the disk and passing through its center?

A $4.00 \mathrm{~kg}$ hollow sphere $\left(\mathrm{I}=2 / 3 \mathrm{MR}^{2}\right)$ is spinning with an angular velocity of $10.0 \mathrm{rad} / \mathrm{s}$ . The diameter of the sphere is $20.0 \mathrm{~cm}$ . The rotational kinetic energy of the spinning sphere is

A person rides a bicycle along a straight road. From the point of view of the rider, what's the direction of the angular momentum vector of the front wheel?

The rotational inertia of a thin rod about one end is $1 / 3 \mathrm{ML}^{2}$ . What is the rotational inertia of the same rod about a point located $0.40 \mathrm{~L}$ from the end?

An $8.00 \mathrm{~kg}$ object has a moment of inertia of $1.50 \mathrm{~kg} \mathrm{~m}^{2}$ . If a torque of $2.00 \mathrm{~N} \cdot \mathrm{m}$ is applied to the object, the angular acceleration is

A $4.00 \mathrm{~kg}$ hollow cylinder of radius $5.00 \mathrm{~cm}$ starts from rest and rolls without slipping down a 30.0 degree incline. If the length of the incline is $50.0 \mathrm{~cm}$ , then the velocity of the center of mass of the cylinder at the bottom of the incline is

A $10 \mathrm{~kg}$ sphere with a $25.0 \mathrm{~cm}$ radius has a moment of inertia of $2 / 5 \mathrm{MR} 2$ . If a torque of $2.0 \mathrm{~N} \cdot \mathrm{m}$ is applied to the object, the angular acceleration is

A torque of $2.00 \mathrm{~N} \cdot \mathrm{m}$ is applied to a $10.0 \mathrm{~kg}$ object to give it an angular acceleration. If the angular acceleration is $1.75 \mathrm{rad} / \mathrm{s}^{2}$ , then the moment of inertia is

Exam 8: Torque and Angular Momentum

A torque of 15.0 N⋅m15.0 \mathrm{~N} \cdot \mathrm{m}15.0 N⋅m is applied to a bolt. The bolt rotates through an angle of 360 degrees. The work done in turning the bolt is

What is the rotational inertia of a solid iron disk of mass 41.0 kg41.0 \mathrm{~kg}41.0 kg with a thickness of 5.00 cm5.00 \mathrm{~cm}5.00 cm and radius of 30.0 cm30.0 \mathrm{~cm}30.0 cm , about an axis perpendicular to the disk and passing through its center?

A person rides a bicycle along a straight road. From the point of view of the rider, what's the direction of the angular momentum vector of the front wheel?

The rotational inertia of a thin rod about one end is 1/3ML21 / 3 \mathrm{ML}^{2}1/3ML2 . What is the rotational inertia of the same rod about a point located 0.40 L0.40 \mathrm{~L}0.40 L from the end?

An 8.00 kg8.00 \mathrm{~kg}8.00 kg object has a moment of inertia of 1.50 kg m21.50 \mathrm{~kg} \mathrm{~m}^{2}1.50 kg m2 . If a torque of 2.00 N⋅m2.00 \mathrm{~N} \cdot \mathrm{m}2.00 N⋅m is applied to the object, the angular acceleration is

A 10 kg10 \mathrm{~kg}10 kg sphere with a 25.0 cm25.0 \mathrm{~cm}25.0 cm radius has a moment of inertia of 2/5MR22 / 5 \mathrm{MR} 22/5MR2 . If a torque of 2.0 N⋅m2.0 \mathrm{~N} \cdot \mathrm{m}2.0 N⋅m is applied to the object, the angular acceleration is

A torque of 2.00 N⋅m2.00 \mathrm{~N} \cdot \mathrm{m}2.00 N⋅m is applied to a 10.0 kg10.0 \mathrm{~kg}10.0 kg object to give it an angular acceleration. If the angular acceleration is 1.75rad/s21.75 \mathrm{rad} / \mathrm{s}^{2}1.75rad/s2 , then the moment of inertia is

A torque of $15.0 \mathrm{~N} \cdot \mathrm{m}$ is applied to a bolt. The bolt rotates through an angle of 360 degrees. The work done in turning the bolt is

What is the rotational inertia of a solid iron disk of mass $41.0 \mathrm{~kg}$ with a thickness of $5.00 \mathrm{~cm}$ and radius of $30.0 \mathrm{~cm}$ , about an axis perpendicular to the disk and passing through its center?

The rotational inertia of a thin rod about one end is $1 / 3 \mathrm{ML}^{2}$ . What is the rotational inertia of the same rod about a point located $0.40 \mathrm{~L}$ from the end?

An $8.00 \mathrm{~kg}$ object has a moment of inertia of $1.50 \mathrm{~kg} \mathrm{~m}^{2}$ . If a torque of $2.00 \mathrm{~N} \cdot \mathrm{m}$ is applied to the object, the angular acceleration is

A $10 \mathrm{~kg}$ sphere with a $25.0 \mathrm{~cm}$ radius has a moment of inertia of $2 / 5 \mathrm{MR} 2$ . If a torque of $2.0 \mathrm{~N} \cdot \mathrm{m}$ is applied to the object, the angular acceleration is

A torque of $2.00 \mathrm{~N} \cdot \mathrm{m}$ is applied to a $10.0 \mathrm{~kg}$ object to give it an angular acceleration. If the angular acceleration is $1.75 \mathrm{rad} / \mathrm{s}^{2}$ , then the moment of inertia is