A block of mass 0.0200 kg is rotating on a flat bench with negligible friction. It is held in the circle by a massless string running through a hollow in the bench. At first, the block is rotating at a radius of 0.350 m from the hollow at an angular speed of 1.95 rad/s. The string is shortened by pulling from below the bench, reducing the rotational radius to 0.180 m. Determine the change in kinetic energy of the block. Treat the block like a particle. 

A uniform rod of length 0.80 m is fixed to a massless axle on one of its ends such that its rotational axis is perpendicular to its length. The rod's moment of inertia about the axle is 0.0410 kg•m². The rod is rotating at 1.40 rads/s when a remote-controlled movable mass slides from very close to the axle to the opposite end of the rod. The mass has a linear speed of 0.980 m/s when located at the opposite end. Determine the mass of the rod. You may treat the mass as a particle. 

A student throws a 5.0 g tip in the x-direction with a speed of 25 m/s toward a square-shaped, vertical swinging plate made of foam, attached to a pivot at one end. The plate has a mass of 125g, and a side of 80 cm. The tip is implanted in the foam 5 cm from the opposite side of the pivot. Calculate the angular speed of the plate just after the collision.  

A 10 kg fox terrier dog runs and jumps through a hoop onto a rotating circular platform in a circus scene. The platform, with a mass of 65 kg and a radius of 1.25 m, rotates at 43 rpm around its frictionless central axis. The dog is trained to run at a speed of 2.0 m/s in the same direction as the platform's rotation and tangent to the platform. The dog lands exactly on the platform's edge. Determine the angular velocity of the platform after the dog has landed on it.

A 47 kg monkey is standing at the center of a disk that is rotating horizontally at an angular velocity of 0.72 rad/s. The moment of inertia of the disk is 840 kg.m² and its radius is 2.0 m. The monkey walks straight to the edge of the disk while the disk rotates without any external forces being applied to it. Given that there is no friction, determine the disk's angular velocity after the monkey reaches the edge.

A 42 kg dog is at the center of a large disk of radius 6.0 m. Initially, the disk rotates horizontally with an angular velocity of 0.82 rad/s about a vertical axis through its center. Afterward, the dog walks directly to the edge of the disk. Given that the moment of inertia of the disk is 870 kg·m², determine the total rotational kinetic energy of the system with the dog initially on the disk at the center first and then do the same for when the dog walks to the edge of the disk. Assume that the disk rotates without any friction.

Imagine a circus performer spinning on a giant rotating platform. The performer's body can be approximated as a solid cylinder with a mass of 60.0 kg, a radius of 0.4 m, and a height of 1.8 m. Each arm can be approximated as a thin rod with a mass of 3.0 kg and a length of 0.7 m. If the performer stands on the platform with arms outstretched and completes one rotation in 2.5 s, what would be the new time for each rotation if the performer brings their arms close to their body? Ignore any frictional effects and assume the platform is weightless.