6.2 Torque and Work

Work and Energy in Rotation

Just as a force can transfer energy linearly through work, a torque can transfer energy rotationally. The work done by a torque changes a body’s rotational energy.

The relationship between torque and angular displacement mirrors that between force and linear displacement.

Important Equation: ${W = \int_{\theta_1}^{\theta_2} \tau(\theta) , d\theta}$

${W}$ = work done by a torque between ${\theta_1}$ and ${\theta_2}$

${\tau(\theta)}$ = torque as a function of angular position

${d\theta}$ = infinitesimal angular displacement

If the torque is constant, this simplifies to: ${W = \tau , \Delta\theta}$