Exam 8: Torque and Angular Momentum

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

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 Jim is exerting to support the stretcher, with Bob on it, is

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

A 10 kg solid cylinder with a 50.0 cm radius has a moment of inertia of 1/2 MR². If a torque of 2.0 N•m is applied to the object, the angular acceleration 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 downward acceleration of m₁?

A 10 kg solid cylinder (I = 1/2 MR²) with a radius of 30.0 cm is rotating about a vertical axis through its center. If the angular momentum is increasing at the rate of 25.0 kg m²/s², then what is the angular acceleration?

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 rotational inertia of this system of masses about the X-axis, perpendicular to the Z-Y plane, is

Chris and Jamie are carrying Wayne on a horizontal stretcher. The uniform stretcher is 2.00 m long and weighs 100 N. Wayne weighs 800 N. Wayne's center of gravity is 75.0 cm from Chris. Chris and Jamie are at the ends of the stretcher. The upward force that Chris is exerting to support the stretcher, with Wayne on it, is

A pole-vaulter holds out a 4.75 m 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 ratio of the force applied by the hand on the end of the pole to the weight of 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 20.0 cm and a moment of inertia of ½ MR². If m₁ is 3.00 kg, m₂ is 6.00 kg and M is 4.00 kg, then what is the tension in the string that is attached to mass m₂?

An auto mechanic is attempting to loosen a bolt in an engine using a large wrench, but to no avail. If she applies a force of 510 N perpendicular to the wrench she is using, applied at 0.75 m from the axis of rotation of the bolt, what is the value of the friction force applied to the outer surface of the bolt's threads? The threaded portion of the bolt has diameter 1.2 cm.

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 25.0 cm and a moment of inertia of ½ MR². If m₁ is 2.00 kg, m₂ is 1.00 kg, M is 4.00 kg, and the angle is 60.0 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 25.0 cm and a moment of inertia of ½ MR². If m₁ is 4.00 kg, m₂ is 4.00 kg, and M is 4.00 kg, then what is the tension in the string attached to m₁?

A 1.500 m long uniform beam of mass 30.00 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 kg mass, m, is attached to the end of the beam. What is the tension in the wire?

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

A 10 kg object has a moment of inertia of 1.25 kg m². If a torque of 2.5 N•m is applied to the object, the angular acceleration is

An 8.0 kg object has a moment of inertia of 1.00 kg m². What torque is needed to give the object an angular acceleration of 1.5 rad/s²?

A 20.0 kg hollow cylinder (I = MR²) has a diameter of 50.0 cm. The cylinder is rolling down a hill with a velocity of 5.00 m/s. The rotational kinetic energy of the rolling cylinder is

A 4.00 kg solid sphere of radius 5.00 cm starts from rest and rolls without slipping down a 30.0 degree incline. The acceleration of the center of mass of the solid sphere is

A 0.50 kg solid disk spins at 250 rpm. A torque of 12.5 N·m is applied for 0.150 s to bring it to rest. What is the disk's radius?