slope. Fortunately, the formula for rotational kinetic energy, much like the formula for
translational kinetic energy, can be a valuable problem-solving tool.
The kinetic energy of a rotating rigid body is:
Considering that I is the rotational equivalent for mass and is the rotational equivalent for
velocity, this equation should come as no surprise.
An object, such as a pool ball, that is spinning as it travels through space, will have both rotational
and translational kinetic energy:
In this formula, M is the total mass of the rigid body and is the velocity of its center of mass.
This equation comes up most frequently in problems involving a rigid body that is rolling along a
surface without sliding. Unlike a body sliding along a surface, there is no kinetic friction to slow
the body’s motion. Rather, there is static friction as each point of the rolling body makes contact
with the surface, but this static friction does no work on the rolling object and dissipates no
energy.
EXAMPLE
A wheel of mass M and radius R is released from rest and rolls to the bottom of an inclined plane of
height h without slipping. What is its velocity at the bottom of the incline? The moment of inertia of a
wheel of mass M and radius R rotating about an axis through its center of mass is^1 / 2 MR^2.Because the wheel loses no energy to friction, we can apply the law of conservation of mechanical
energy. The change in the wheel’s potential energy is –mgh. The change in the wheel’s kinetic
energy is. Applying conservation of mechanical energy:
It’s worth remembering that an object rolling down an incline will pick up speed more slowly than