A constant torque of 3 Nm is applied to an unloaded motor at rest at time t = 0. The motor reaches a speed of 1,393 rpm in 4 s. Assuming the damping to be negligible, calculate the motor inertia in Nm·s2.

The moment of inertia of the motor is 0.0823 Newton-meter-square seconds.

Explanation:

From Newton's Laws of Motion and Principle of Motion of D'Alembert, the net torque of a system (), measured in Newton-meters, is:

(1)

Where:

- Moment of inertia, measured in Newton-meter-square seconds.

- Angular acceleration, measured in radians per square second.

If motor have an uniform acceleration, then we can calculate acceleration by this formula:

(2)

Where:

- Initial angular speed, measured in radians per second.

- Final angular speed, measured in radians per second.

- Time, measured in seconds.

If we know that , , and , then the moment of inertia of the motor is:

The moment of inertia of the motor is 0.0823 Newton-meter-square seconds.