Two masses are attached to a 1 m massless rod on a flat frictionless table. A 3 kg mass is on the left end, while the 5 kg mass is on the right end. The axis of rotation is 0.25 m away from the 3 kg mass. Given that F1 = 5 N, F2 = 3 N (which is located halfway between the axis of rotation and the 5 kg mass, and F3 = 4 N, calculate the total torque, moment of inertia, and the resulting angular acceleration.

Two thin rectangular sheets (0.20 m x 0.47 m) are identical. In the first sheet the axis of rotation lies along the 0.20-m side, and in the second it lies along the 0.47-m side. The same torque is applied to each sheet. The first sheet, starting from rest, reaches its final angular velocity in 2.3 s. How long does it take for the second sheet, starting from rest, to reach the same angular velocity? Number i Units

An object has a moment of inertia of 0.79 kg m2. Its angular velocity is increasing at the rate of 0.40 rad/s per second. What is the net torque (in N m2) on the object?

Consider a person who is sitting on a frictionless rotating stool. The person initially has his arms outstretched and is rotating with an angular speed of 5.0 rad/s. He then pulls his arms close to his body, thus reducing his moment of inertia to 80% of the initial one. What is his final angular speed?

Ice skaters can increase the angular speed of their spins by pulling their arms towards their body.  A skater with their arms extended has a moment of inertia of 2.49 kg m2 and a moment of inertia of 0.77 kg m2 after pulling their arms in.  If a skater begins a spin with their arms extended such that they are rotating with an angular speed of 2.07 rad/s, what will their rotation speed be when they pull their arms in?

A student holds a bike wheel and starts it spinning with an initial angular speed of 9.0rotations per second. The wheel is subject to some friction, so it gradually slows down. In the 10 s period following the inital spin, the bike wheel undergoes 70 complete rotations. Assuming the frictional torque remains constant, how much more time Δts will it take the bike wheel to come to a complete stop? The bike wheel has a mass of 0.625 kg and a radius of 0.315 m. If all the mass of the wheel is assumed to be located on the rim, find the magnitude of the frictional torque τf that was acting on the spinning wheel.

A circular disk with a radius of 0.38 m is subject to 2 tangentially applied forces. The disc is fixed such that it will rotate about its center. Both forces produce a torque in the same direction. The mass of the disc is 0.73 kg. The moment of inertia of a disc is I =1/2MR^2 F1 = 2.3 N applied at the outer edge of the disc. F2 = 3.6 N applied at a distance of 0.29 from the center of the disc. What is the angular acceleration of the disc?

A capstan is a device used on old sailing ships to raise the anchor. A sailor pushes the long lever, turning the capstan and winding up the anchor rope. If the capstan turns at a constant speed, the net torque on it, is zero. The rope tension due to the weight of the anchor is 1500 N. The distance from the axis to the point on the lever where the sailor pushes is seven times the radius of the capstan around which the rope is wound.With what force must the sailor push in order to turn the capstan at a constant speed, meaning that the net torque on the capstan is zero?

When you hold an ball by only your forearm, the main lifting muscle in your arm is the biceps. Suppose the mass of a forearm with hand is 1.80 kg. The biceps is connected to the forearm a distance of 2.50 cm from the elbow, and it holds a 44.5 N (about 10 lbs) ball at the end of the forearm at distance of 35.0 cm from the elbow. What is the magnitude of the torque about the elbow by the ball, in N·m? Use g = 10.0 m/s2. Your answer needs to have 3 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement.

Modern wind turbines generate electricity from wind power. The large, massive blades have a large moment of inertia and carry a great amount of angular momentum when rotating. A wind turbine has a total of 3 blades. Each blade has a mass of m = 5500 kg distributed uniformly along its length and extends a distance r = 44 m from the center of rotation. The turbine rotates with a frequency of f = 15 rpm. Calculate the angular momentum of the wind turbine, in units of kilogram meters squared per second.