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 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 $m_{1}$ ?

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

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?

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 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 $\mathrm{m}_{1}$ ?

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 $\mathrm{m}_{2}$ ?

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 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 $\mathrm{m}_{1}$ ?

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?

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

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

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 $\mathrm{m}_{1}$ ?

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

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