Traagheidsmoment

When a rigid body is in linear motion, every point moves with the same velocity. However, when it is in rotational motion, different points on the body have different velocities and therefore different kinetic energies.

If the i-th particle, placed at a perpendicular distance r_i from the axis of rotation, has a tangential velocity of v_i, its kinetic energy is calculated by replacing v_i with the product of angular speed and r_i.

The total kinetic energy of the rigid body is the sum of the individual kinetic energies of the constituent particles. Since angular speed is the same for each particle, it can be pulled out of the summation.

On comparing this equation with the kinetic energy equation for translational motion, a new rotational variable is defined. This quantity is called the moment of inertia and has units of kilogram meters squared.

For a single particle rotating about a fixed axis, the moment of inertia is the product of its mass and the square of its distance from the axis of rotation.