5.6 Newton’s Second Law in Rotational Form

In linear motion, Newton’s Second Law is ${F_{net} = m a}$.

In rotational motion, torque plays the role of force, and angular acceleration replaces linear acceleration:

Important Equation: ${\tau_{net} = I_{sys} \alpha_{sys}}$

${\tau_{net}}$ = net external torque acting on the system

${I_{sys}}$ = total rotational inertia of the system

${\alpha_{sys}}$ = angular acceleration of the system

This relationship is the rotational equivalent of Newton’s Second Law, showing that the rate of change of angular velocity is proportional to the net torque, inversely weighted by the object’s resistance to rotation.