A thin cylindrical ring starts from rest at a height h₁ = 81 m. The ring has a radius R = 6 cm and a mass M = 2 kg.

1. If the ring rolls (without slipping) all the way to point 2, what is the ring's energy at point 2 in terms of h₂ and v₂?

2. Given h₂ = 8 m, what is the velocity of the ring at point 2 in m/s?

3. What is the ring's rotational velocity in rad/s at point 2?

4. After passing point 2 the hill becomes frictionless and the ring's rotational velocity remains constant. What is the linear velocity of the ring at point 3 in m/s?

R h, 2