8.3. A diver has a mass of 70 kg. In 'tuck' position, we can treat this mass as a disc of radius 0.50 m, but when fully extended, the diver is more like a rod of length 2.4 m. (a) Compare the rotational inertia of this diver in tuck position to their rotational inertia when fully extended. (b) If this diver ends their dive fully extended and is rotating at 0.85 rotations/s, what was their rotational speed earlier in the dive when they were in tuck position? (c) Does the transition from tuck to fully extended require extra energy to be provided by the diver's muscles?

A Fall on the Moon. You and your team are stationed at an earth-based mission control facility and have been tasked with assisting astronauts via radio communication as they exit a spacecraft that has recently landed on the moon. The astronauts intended to explore the lunar surface but, unfortunately, they hit a snag even before they opened the hatch. Their craft has landed right on the edge of a 15-ft cliff, so that there is no way off the lander except to drop that distance from the bottom rung of a ladder on the side of the ship. You look up the structural parameters of the space suits, the gear they are wearing, and the physical limitations of the crew, and find that, on earth, the maximum drop they can safely endure is 4.0 ft. (a) Is it safe for them to make the 15-ft drop on the moon? (b) What is the maximum drop they can safely endure on the moon? Note that the acceleration due to gravity on the moon is one-sixth as large as that on earth.

Show work to find the gravitational acceleration a distance z from the center of a uniform disk with mass M and radius a.

Can you show me how to solve this?