Moment of Inertia

Moment of Inertia:

Increasing the mass increases the moment of inertia, symbolized by I, which is sometimes called the rotational inertia of an object. But the distribution of the mass is more important, i.e. distributing the mass further from the centre of rotation increases the moment of inertia by a greater degree. The moment of inertia is measured in kilogram metre² (kg m²).

The energy required or released during rotation is the torque times the rotation angle; the energy stored in a rotating object is one half of the moment of inertia times the square of the angular velocity. The power required for angular acceleration is the torque times the angular velocity.

Torque

Torque τ is the twisting effect of a force F applied to a rotating object which is at position r from its axis of rotation. Mathematically,

τ = r × F

Where × denotes the cross product. A net torque acting upon an object will produce an angular acceleration of the object according to

τ = Iα

Just as F = ma in linear dynamics.