The net work done in accelerating a rotating object from rest to an angular speed of 204.22 s^-1 is 5.15 kJ. What is the moment of inertia of the object?

A 0.45 kg tetherball is attached to a pole and rotating in a horizontal circle of radius r₁ = 1.4 m and is circling at angular speed = 1.42 rad/s. As the rope wraps around the pole the radius of the circle shortens and became r2 = 0.9 m, that decreases the moment of inertia of the rotating tetherball. What is the moment of inertia of the rotating ball before the rope is wrapped around the pole measured in kgm² (answer with 3 decimal places)?

The figure above shows Einstein spinning on a platform. He is initially spinning at a rate of 1rev/s, and holding his hands a distance of R1 = 80.3 cm away from his body. He then pulls his arms in to a distance of R2 = 40cm, changing his rotational speed. In this problem you can model Einstein’s body as a cylinder with a moment of inertia I = 30MR2, where M is his mass (60kg), and R is the distance his hands are from his body. (Notice that the figure shows him holding weights, but we are going to assume they are massless, to make it simpler!)(a) If he draws his arms in very quickly, you can safely ignore any frictional force on the platform. Assuming this is true, how fast is he rotating after he draws his arms in? (b)  In reality, after he draws his arms in friction will start to slow him down. If this small amount of friction is applying a torque of 4 Nm to the platform, how long would it take before Einstein stops moving?

A solid disk rotates in the horizontal plane at an angular velocity of 4.20 × 10-2 rad/s with respect to an axisperpendicular to the disk at its center. The moment of inertia of the disk is 0.14 kg.m2. From above, sand is droppedstraight down onto this rotating disk, so that a thin uniform ring of sand is formed at a distance of 0.40 m from the axis.The sand in the ring has a mass of 0.50 kg. After all the sand is in place, what is the angular velocity of the disk?