Obtain an expression for the work done by a torque. Hence write the expression for power.

The work done by a torque in rotating an object depends on the torque applied and the angular displacement through which the object rotates. If a torque is applied to a body, that body would rotate about an axis. The amount of work done is directly proportional to both the magnitude of the torque and the angle through which the object moves. In essence, if a greater torque is applied or if the object rotates through a larger angle, more work is done.

Power, on the other hand, measures the rate at which this work is done. It is defined as the rate at which work is being done over time. For the case of rotational motion, power is related to the work done by the torque and also the time taken to that work. To be more specific, power will be calculated in terms of how much work is done within a certain given time frame when an object is rotated.

This implies that the power developed in a rotating system is dependent on the torque applied to the object as well as its speed of rotation. Understanding torque, work, and power interdependence is thus very important for the analysis of rotational systems and their efficiency in doing work.

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