Miscellaneous physics question

1. Competitive divers pull their limbs in a curl up their bodies when they do flips. Just before entering the water, they fully extend their limbs to enter straight down. Explain the effect of both actions on their angular velocity. What is the effect of these actions on their angular momentum?

2. What is the final velocity of a hoop that rolls without slipping down a 5.00 m high hill, starting from rest?

3. Three children are riding on the edge of a 1.60-m-radius, 100 kg merry-go-round, spinning at 20.0 rpm. The children have masses of 22.0, 28.0, and 33.0 kg. If the child with a mass of 28.0 kg moves to the center of the merry-go-round, what is the new angular velocity in rpm?

4. A ball slides up a ramp without friction. It is then rolled without slipping and with the same initial velocity up another ramp. In which case does it reach a greater height, and why?

5. (a) Calculate the angular momentum of the earth in its orbit around the sun. (b) Compare this with the angular momentum of the earth on its axis.

6. A yo-yo may be modeled as a small cylinder of mass 0.12 kg and radius 8.0 cm. (A) What is the rotational inertia of such a yo-yo? (B) As the yo-yo unwinds from the string, its angular speed goes up, from 0 to 40 radians per second in a period of 1.4 seconds. What is the net torque on the yo-yo? (C) What is the yo-yo's angular momentum at the end of the period described above? (D) When the yo-yo is rotating at 40 radians per second, how many revolutions is it making each second?