Rotational Kinetic Energy

This formula gives the energy an object has because it is spinning. It comes from adding up the kinetic energy of every tiny part of the body, where parts farther from the axis move faster; the moment of inertia captures how the mass is distributed, and angular velocity tells how fast the rotation is. A larger moment of inertia or a faster spin both increase the rotational energy, with speed having a squared effect.

Use this when you need the energy stored in rotation, such as for wheels, shafts, discs, spinning tools, or rotating machinery. It is also useful in physics problems involving rolling motion, because rolling objects often have both translational and rotational kinetic energy.

• Using ordinary speed instead of angular velocity in radians per second
• Forgetting to square ω, which makes the result much too small
• Using the wrong moment of inertia formula for the object's shape