### Moments of Inertia

- Inertia is defineed as the property of an object to resist changes on motion.
- The ability of an object to continue to stay at rest or in its existing state of rest or uniform motion in a straight line.
- Unless that state is changed by an external, unbalanced force.
- Rotational Inertia measures the ability of an object to resist rotating about a fixed pint around a circular path.
- The moment of inertia is the ability of an object to resist a change in its angular acceleration.
- A torque is a force applied to an object, in a circular path, capable of alterning its moment of inertia or angular acceleration.

The total rotational torque taken at the center of gravity of a complex rotating object can be expressed as the sum of all torques acting on individual parts of the rotating object.

The illustration below is of a rectangular object rotating about a point C.

The object can be taken a s a whole or broken up into smaller masses, each rotating about slightly different radius from the center of rotation.

For the system above, for example,

**Example**:

Two masses are suspended on a nylon thread of negligible mass as shown.

Find the moment of Inertia and the total torque of the system if it completes 20 revolutions in 10 s.

m1 = 0.12 Kg

m2 = 0.36 Kg

r1 = 0.1 m

r2 = 0.75 m

**Solution:**

a) Find the moment of inertia I

b) Find the total Torque

**First find the angular acceleration a**