It has been suggested that rotating cylinders about 12.5 mi long and 3.99 mi in diameter be placed in space and used as colonies. What angular speed must such a cylinder have so that the centripetal acceleration at its surface equals the free-fall acceleration on Earth

If you were to drop a rock from a tall building, assuming that it had not yet hit the ground, and neglecting air resistance. what is its vertical displacement (in m) after 6 s?

Adiver in midair has an angular velocity of 6.0 rad/s and a moment of inertia of 1.2 kg·m2. he then pulls is arms and legs into a tuck position and his angular velocity increases to 12 rad/s. the net external torque acting on the diver is zero. what is his moment of inertia in the tuck position?

Aforce of 200 n is applied to an input piston of cross-sectional area 2 sq. cm pushing it downward 2.8 cm. how far does the output piston of cross-sectional area 12 sq. cm move upward? show all work.