Racing right circular cylindrical objects on inclined plane

We can now predict the translational velocity of right circular cylindrical objects rolling down an incline. We use energy conservation here. We consider the following initial and final conditions:

Initial Condition:

Object at rest at height, h over ground level.

Final Condition:

Object rolling with speed v at h=0 level. After rolling without sliding to ground level we have rotational and translational kinetic energy:

Because there are no dissipative forces involved we have

and solving for v we get

We see that objects with larger moment of inertia have smallest final velocity. We check this prediction by racing various right circular object against each other. We see for example that the solid disk coms down faster than the hoop. Note that the mass of the object does not matter here (as usual). All that matters is how the mass is distributed about the axis of rotation; the closer (on average) the bulk is to the axis of rotation the faster the object makes it down the incline since more of the potential energy is converted to translational potential energy and less to rotational poential energy.