Exam 8: Torque and Angular Momentum

A 1.5 m long, 0.75 kg 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 net torque on the rod about the pivot?

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 1.00 kg, m₂ is 2.00 kg, M is 4.00 kg, and the angle is 60.0 degrees, then what is the acceleration of m₁?

A torque of 2.00 N•m is applied to a 10.0 kg object to give it an angular acceleration. If the angular acceleration is 1.75 rad/s², then the moment of inertia is

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 1.2 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 system in equilibrium cannot have

A torque of 15.0 N^.m is applied to a bolt. The bolt rotates through an angle of 360 degrees. The work done in turning the bolt is

A 4.00 kg hollow 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 hollow sphere is

A centrifuge has a rotational inertia of 5.50 × 10⁻³ kg m². How much energy must be supplied to bring it from rest to 500 rad/s?

A 5.00 kg object has a moment of inertia of 1.20 kg m². What torque is needed to give the object an angular acceleration of 2.0 rad/s²?

A 6.00 kg mass is located at (1.0 m, −2.00 m, 3.00 m), a 5.00 kg mass is located at (1.0 m, 3.00 m, −2.00 m), and a 4.00 kg mass is located at (−1.0 m, −2.00 m, 2.00 m). The center of gravity of the system of masses 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 X-axis, perpendicular to the Z-Y plane, is