- A uniform solid sphere is released from rest at the top of a 2.5 m long board that is inclined at 22° above the horizontal. The mass of the sphere is 25 kg and the radius is 12 cm, (a) what is the moment of inertia of the sphere? Then neglecting energy losses calculate the following values once the sphere has reached the bottom of the incline assuming that it rolls without slipping: (b) the translational speed of the center of mass, and (c) the angular speed of the sphere about its center of mass. Include a relevant diagram of the situation. [Diagram 2 pts.]

A solid, uniform disk of radius 0.250 m and mass 55.0 kg rollsdown a ramp of length 4.50 m that makes an angle of 15.0°with the horizontal. The disk starts from rest from the top ofthe ramp. Find (a) the speed of the disk’s center of mass whenit reaches the bottom of the ramp and (b) the angular speedof the disk at the bottom of the ramp.

a) A diver leaps from a platform and immediately goes into a tuck position. If we assume that the diver has an initial angular velocity of 7.5 rad/sec, and has an angular acceleration of -0.22rad/sec2,how long will it take for the diver to complete 2 full revolutions?b) Assume that the diver is 6 m above the water with an initial vertical velocity of 1.74 m/s when she begins to rotate. Will she be able to complete 2 full revolutions before hitting the water? Why or why not?

In the figure, a constant horizontal force  F→app of magnitude 31.0 N is applied to a uniform solid cylinder by fishing line wrapped around the cylinder. The mass of the cylinder is 17.5 kg, its radius is 0.656 m, and the cylinder rolls smoothly on the horizontal surface. (a) What is the magnitude of the acceleration of the center of mass of the cylinder? (b) What is the magnitude of the angular acceleration of the cylinder about the center of mass? (c) In unit-vector notation, what is the frictional force acting on the cylinder?