A solid uniform cylinder of mass 3.25 kg, diameter 65.0 cm and length 12.4 cm, is connected to a block of mass 1.50 kg by a massless string passing over two frictionless pulleys, as shown below. The string is wrapped around the cylinder and doesn’t slip. The cylinder is free to rotate about an axis through its center perpendicular to its circular faces, and the system is released from rest. A. Draw free body diagrams for the cylinder and for the block. B. What is the acceleration of the block after it is released?
C. How far must the 1.50 kg block fall before it reaches a speed of 2.50 m/s?
D. How fast is the cylinder turning at this instant (i. e. at the instant the block is moving at 2.50 m/s)?
The rotational inertia of a solid cylinder of mass M and radius R rotating about its central axis is I = 2 1/2MR

Your starship, the aimless wanderer, lands on the mysterious planet mongo. as chief scientist-engineer, you make the following measurements: a 2.50-kg stone thrown upward from the ground at 14.0 m/s returns to the ground in 5.70 s ; the circumference of mongo at the equator is 2.20×10^5 km ; and there is no appreciable atmosphere on mongo. (a) the starship commander, captain confusion, asks for the following information: what is the mass of mongo? (b) if the aimless wanderer goes into a circular orbit 2.20×10^4 km above the surface of mongo, how many hours will it take the ship to complete one orbit? (c) an unmanned spacecraft is in a circular orbit around the moon, observing the lunar surface from an altitude of 44.0 km . to the dismay of scientists on earth, an electrical fault causes an on-board thruster to fire, decreasing the speed of the spacecraft by 23.0 m/s . if nothing is done to correct its orbit, with what speed (in km/h) will the spacecraft crash into the lunar surface?