W = Tθ; P = Tω Awareness that frictional torque has to be taken into…

The idea

For rotation, work done by a constant torque T through an angular displacement θ is W = Tθ, and power is P = Tω, where ω is angular velocity. These equations mirror linear W = Fs and P = Fv. In rotating machinery, frictional torque opposes motion, so the net torque is the applied torque minus the frictional torque. This reduces the useful work output and power delivered. They should also interpret efficiency as the ratio of useful output to total input, recognising that friction causes energy dissipation as thermal energy.

What earns the marks

• Recalls and applies W = Tθ for work done by a constant torque through an angular displacement.
• Recalls and applies P = Tω for mechanical power in rotational motion.
• Converts angular displacement between degrees and radians correctly when using W = Tθ.
• Explains that frictional torque opposes rotation and must be subtracted from the applied torque to find the net torque.
• Calculates useful work or power by using the net torque after accounting for friction.
• Relates energy lost to friction to heating of components and reduced efficiency of the machine.

Common mistakes and how to put them right

• Using degrees directly in W = Tθ without converting to radians.

  Put it right: Convert θ to radians before substitution.

• Ignoring frictional torque and using the applied torque as the net torque.

  Put it right: Subtract the frictional torque to find the net torque.

• Confusing torque with force or angular velocity with linear velocity.

  Put it right: Use the rotational definitions T, θ and ω consistently.

Exam tips

• Write down the equation W = Tθ or P = Tω before substituting values, and check that θ is in radians.
• When friction is present, calculate the net torque first, then use it in the work or power equation.
• State clearly whether you are calculating total input work or useful output work, and show how friction affects the result.