Exam 8: Torque and Angular Momentum

A mass m₁ is connected by a light string that passes over a pulley of mass M to a mass m₂ 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 30.0 cm and a moment of inertia of MR². If m₁ is 4.00 kg, m₂ is 4.00 kg, M is 4.00 kg, and the angle is 70.0 degrees, then what is the acceleration of m₁?

A mass m₁ is connected by a light string that passes over a pulley of mass M to a mass m₂ 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 cm and a moment of inertia of ½ MR². If m₁ is 4.00 kg, m₂ is 2.00 kg, and M is 4.00 kg, then what is the downward acceleration of m₁?

A 2.00 kg mass is located at (4.00 m, 0.00 m, 0.00 m) and a 4.00 kg mass is located at (0.00 m, 3.00 m, 0.00 m). The center of gravity of the system of masses is

A 55 kg girl swings on a swing, whose seat is attached to the pivot by 2.5 m long rigid rods (considered to be massless in this problem). As she swings, she rises to a maximum height such that the angle of the rods with respect to the vertical is 32 degrees. What is the maximum torque on the rods due to her weight, as she moves during one cycle of her swinging from the bottom of her swing path to the highest point?

A pirate demands that his 75 kg prisoner "walk the plank". The prisoner walks out on an 8.0 m long, 50 kg horizontal board that juts out from the side of the pirate ship. If he walks out and stands 7.5 m from the place where the board is connected to the ship's side, what is the net torque applied to the board?

A 3.00 kg hollow sphere of radius 5.00 cm starts from rest and rolls without slipping down a 15.0 degree incline. If the length of the incline is 100 cm, then the velocity of the center of mass of the hollow sphere at the bottom of the incline is

A mass m₁ is connected by a light string that passes over a pulley of mass M to a mass m₂ 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 cm and a moment of inertia of ½ MR². If m₁ is 1.00 kg, m₂ is 2.00 kg, and M is 4.00 kg, then what is the tension in the string attached to m₂?

A 4.00 kg solid sphere (I = 2/5 MR²) is spinning with an angular velocity of 23.0 rad/s. The diameter of the sphere is 20.0 cm. The rotational kinetic energy of the spinning sphere is

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

The rotational inertia of a thin rod about one end is 1/3 ML². What is the rotational inertia of the same rod about a point located 0.300 L from the end?

A pole-vaulter holds out a 5.5 kg, 4.75 m long pole horizontally in front of him. Assuming the pole is uniform in construction, and that he holds the pole with one hand at the very end, and one hand 0.75 m from the end, what is the torque applied by the gravitational force to the pole?

A mass m₁ is connected by a light string that passes over a pulley of mass M to a mass m₂ 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 cm and a moment of inertia of MR². If m₁ is 4.00 kg, m₂ is 3.00 kg and M is 6.00 kg, then what is the tension in the string that is attached to m₁?

A 75.0 kg ladder that is 3.00 m long is placed against a wall at an angle theta. The center of gravity of the ladder is at a point 1.20 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?

A 20.0 cm wrench is used to generate a torque at a bolt. A force of 50 N is applied at the end of the wrench at an angle of 60.0 degrees to the wrench. The torque generated at the bolt is

A thin rod is pivoted around its end, and an identical rod around its center. If they are to have the same rotational kinetic energy, then ω_end/ω_center =

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

A brake pad is used to give a normal force of 150 N to the outer surface of a 0.25 kg spinning disk, in order to slow it down from 250 rpm to rest. The disk's radius is 0.25 m. If the coefficient of friction between the pad and the disk is 0.45, how much time is required for the disk to slow from 250 rpm to rest?

A 2.00 m long horizontal uniform beam of mass 20.0 kg is supported by a wire as shown in the figure. The wire makes an angle of 20.0 degrees with the beam. Attached to the beam 1.40 m from the wall is a ball with a mass of 40.0 kg. What is the tension in the string?

Jim and Mary are carrying Bob on a horizontal stretcher. The uniform stretcher is 2.00 m long and weighs 80 N. Bob weighs 600 N. Bob's center of gravity is 80 cm from Mary. Jim and Mary are at the ends of the stretcher. The upward force that Mary is exerting to support the stretcher, with Bob on it, is

A fire fighter tightens the nut on the top of a fire hydrant using a large wrench. If she applies a force of 250 N perpendicular to the wrench, at a point 0.75 m from the axis of rotation of the nut, how much work does she do on the nut as she rotates it through 45°?