AP Physics 1- 6.2 Torque and Work- Study Notes- New Syllabus

Work by Torque

A torque can transfer energy into or out of an object or rigid system if the torque is exerted over an angular displacement.

Key Points:

• The work done on a rigid system by a torque depends on both the magnitude of the torque and the angular displacement during which it acts.
• Work is done only by the component of torque in the direction of angular displacement.
• Work by torque is a scalar quantity; it may be positive, negative, or zero depending on the relative sense of torque and displacement.
• Positive work: torque and angular displacement act in the same rotational sense.
• Negative work: torque and angular displacement act in opposite rotational senses.

Relevant Equation:

\( W = \tau \, \theta \)

where:

• \( W \) = work done by torque (J)
• \( \tau \) = constant torque applied (N·m)
• \( \theta \) = angular displacement (radians)

Graphical Representation:

• The work done on a rigid system by a given torque can also be found from the area under the curve of a graph of torque as a function of angular displacement.
• This is analogous to the way linear work can be found from the area under the force–displacement curve.