5.10. Kinetic energy of a rotating body

The kinetic energy of a body moving in an arbitrary way is equal to the sum of the kinetic energies of all n material points on which this body can be broken:

If the body rotates around a fixed axis with an angular velocity , then the linear velocity of the i-th point is where , is the distance from this point to the axis of rotation. Consequently.

(5.11)

Where - moment of inertia of the body relative to the axis of rotation.

In the general case, the motion of a rigid body can be represented as the sum of two motions — a translational with a velocity equal to the velocity center of inertia of the body, and rotation with angular velocity   around the instantaneous axis passing through the center of inertia. The expression for the kinetic energy of the body is converted to

(5.12)

Where - moment of inertia of the body relative to the instantaneous axis of rotation passing through the center of inertia.