Exam 8: Torque and Angular Momentum

A 4.00 kg hollow sphere 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 hollow sphere at the bottom of the incline is

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 are the vertical and horizontal components of the force of the wall on the beam at the hinge?

A 5.00 kg mass is located at (2.00 m, 0.00 m, 3.00 m) and a 2.00 kg mass is located at (0.00 m, 4.00 m, -2.00 m). The center of gravity of the system of masses is

A 1.5m long dowel is pivoted about the end so that it is a pendulum of sorts - it can freely swing in a vertical plane. At the other end of the dowel is a brass weight having mass 1.5 kg. (The center of the brass weight is 1.5 m from the pivot point. When the rod is positioned in its swing such that its angle with the vertical is 22.5 degrees, what is the torque on the rod about the pivot due to the presence of the brass weight?

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

A piston in an internal combustion engine applies torque during 150° of each full rotation of the crankshaft to which it is connected. Suppose an 8-cylinder engine (8 such pistons) is running with its crankshaft turning at 2500 rpm and produces 410 J of work each second. What is the average torque applied to the crank shaft by one of the engine's eight pistons?

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 m, 3.00 m, 0.00 m). The rotational inertia of this system of masses about the Y-axis, perpendicular to the X-Z plane, is

A grinding wheel has a mass of 250 kg and moment of inertia of 500 kg m². A torque of 100 N•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 4.00 kg hollow cylinder 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 cylinder is

An ice dancer with her arms stretched out starts into a spin with an angular velocity of 1.00 rad/s. Her moment of inertia with her arms stretched out is 2.48 kg m². What is her angular velocity when she pulls in her arms to make her moment of inertia 1.40 kg m²?

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 0.40 L from the end?

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

A 2.00 kg solid sphere (I = 2/5 MR²) with a diameter of 50.0 cm is rotating at an angular velocity of 5.0 rad/s. The angular momentum of the rotating sphere 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. If the length of the incline is 50.0 cm, then the velocity of the center of mass of the solid sphere at the bottom of the incline is

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 kg m²/s², then what is the torque?

Which of the following objects has the greatest rotational kinetic energy? Each has mass M and radius R, and rotates with angular velocity ω.

A 5.00 kg mass is located at (2.00 m, 0.00 m, 0.00 m) and a 3.00 kg mass is located at (0.00 m, 4.00 m, 0.00 m). The center of gravity of the system of masses is

A 2.000 m long horizontal uniform beam of mass 20.00 kg is supported by a wire as shown in the figure. The wire makes an angle of 20.00 degrees with the beam. Attached to the beam 1.400 m from the wall is a ball with a mass of 40.00 kg. What are the vertical and horizontal components of the force of the wall on the beam at the hinge?

A 25.0 kg propeller may be considered to be a 4.5 m long, thin rod, spun about its center. Assuming the propeller starts from rest, What angular velocity will it have if a torque of 1100 N·m is applied for 1.2 s?

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 downward acceleration of m₁?