In the action adventure film Indiana Jones and the Raiders of the Lost Ark, Indiana Jones searches for the Ark of the Covenant. In one well-known nail biting scene Indiana tries to escape being crushed by a huge boulder rolling down a sloping terrain inside a tunnel. The rolling boulder of mass m rolls down the only path that Indiana Jones can take. Assume that the friction force between the sphere and the surface of the hill is negligible.

At a particular time t₁ the spherical boulder is at location 1 and moving with velocity v₁. At a later time t₂ the sphere is at location 2 and moving with velocity v₂. Locations 1 and 2 are at vertical heights h1 and h2respectively, from the bottom of the tunnel.

When answering the following questions use 1 and 2 for subscripts to identify the different variables at the two different locations.

What is the equation for the rotational kinetic energy K_R,1 of the spherical boulder?