Exam 8: Torque and Angular Momentum

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 Z-axis, perpendicular to the X-Y plane, is

A $10 \mathrm{~kg}$ solid cylinder with a $50.0 \mathrm{~cm}$ radius has a moment of inertia of $1 / 2 \mathrm{MR}^{2}$ . If a torque of $2.0 \mathrm{~N} \bullet \mathrm{m}$ 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 $1.00 \mathrm{~kg}, \mathrm{~m}_{2}$ is $2.00 \mathrm{~kg}$ , and M is $4.00 \mathrm{~kg}$ , then what is the tension in the string attached to $\mathrm{m}_{2}$ ?

A $30.0 \mathrm{~cm}$ wrench is used to generate a torque at a bolt. A force of $50.0 \mathrm{~N}$ is applied at the end of the wrench at an angle of 70.0 degrees. The torque generated at the bolt is

A $4.00 \mathrm{~kg}$ hollow sphere of radius $5.00 \mathrm{~cm}$ starts from rest and rolls without slipping down a 30.0 degree incline. The acceleration of the center of mass of the hollow sphere is

A $5.00 \mathrm{~kg}$ mass is located at $(1.0 \mathrm{~m}, 0.00 \mathrm{~m}, 3.00 \mathrm{~m})$ , a $2.00 \mathrm{~kg}$ mass is located at $(0.00 \mathrm{~m}, 3.00 \mathrm{~m},-2.00$ $\mathrm{m})$ , and a $3.00 \mathrm{~kg}$ mass is located at $(-1.0 \mathrm{~m},-2.00 \mathrm{~m}, 0.00 \mathrm{~m})$ . The center of gravity of the system of masses 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 minimum angle the ladder must make with the horizontal for the ladder not to slip and fall?

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 incline 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 $2.00 \mathrm{~kg}, \mathrm{~m}_{2}$ is $1.00 \mathrm{~kg}, \mathrm{M}$ is $4.00 \mathrm{~kg}$ , and the angle is 60.0 degrees, then what is the acceleration of $m_{1}$ ?

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 $\mathrm{M}$ is $4.00 \mathrm{~kg}$ , then what is the downward acceleration of $m_{1}$ ?

A $30.0 \mathrm{~cm}$ wrench is used to generate a torque at a bolt. A force of $40 \mathrm{~N}$ is applied perpendicularly at the end of the wrench. The torque generated at the bolt 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. The acceleration of the center of mass of the cylinder 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 center of gravity of the system of masses 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 $1.2 \mathrm{~m}$ from the base of the ladder. The coefficient of static friction at the base of the ladder is 0.400 . There is no friction between the wall and the ladder. What is the minimum angle the ladder must make with the horizontal for the ladder not to slip and fall?

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 $30.0 \mathrm{~cm}$ and a moment of inertia of $\mathrm{MR}^{2}$ . If $\mathrm{m}_{1}$ is $4.00 \mathrm{~kg}, \mathrm{~m}_{2}$ is $3.00 \mathrm{~kg}$ and $\mathrm{M}$ is $6.00 \mathrm{~kg}$ , then what is the tension in the string that is attached to $m_{1}$ ?

A $4.00 \mathrm{~kg}$ solid sphere ( $\left.\mathrm{I}=2 / 5 \mathrm{MR}^{2}\right)$ is spinning with an angular velocity of $23.0 \mathrm{rad} / \mathrm{s}$ . The diameter of the sphere is $20.0 \mathrm{~cm}$ . The rotational kinetic energy of the spinning sphere is

A $8.0 \mathrm{~kg}$ object has a moment of inertia of $1.00 \mathrm{~kg} \mathrm{~m}^{2}$ . What torque is needed to give the object an angular acceleration of $1.5 \mathrm{rad} / \mathrm{s} 2$ ?

A $2.00 \mathrm{~kg}$ solid sphere $\left(\mathrm{I}=2 / 5 \mathrm{MR}^{2}\right)$ with a diameter of $50.0 \mathrm{~cm}$ is rotating at an angular velocity of 5.0 $\mathrm{rad} / \mathrm{s}$ . The angular momentum of the rotating sphere is

A $6.00 \mathrm{~kg}$ mass is located at $(1.0 \mathrm{~m},-2.00 \mathrm{~m}, 3.00 \mathrm{~m})$ , a $5.00 \mathrm{~kg}$ mass is located at $(1.0 \mathrm{~m}, 3.00 \mathrm{~m},-2.00$ $\mathrm{m})$ , and a $4.00 \mathrm{~kg}$ mass is located at $(-1.0 \mathrm{~m},-2.00 \mathrm{~m}, 2.00 \mathrm{~m})$ . The center of gravity of the system of masses is

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 $0.300 \mathrm{~L}$ from the end?

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 Y-axis, perpendicular to the Z-X plane, is