Why It Matters: Rotational Newton’s Second Law

A point particle, where all the mass is concentrated at a single point, can only move translationally.  As a result, the translational version of Newton’s second law, `\Sigma \vec{F} = m \vec{a}`, completely describes how the forces act on a point particle to cause its motion.  For an extended object like a rigid body, however, not only can the center of mass move, but it can also rotate about its center of mass.  Because the extended object is capable of two types of motion, we need an additional equation we can use to describe how the object rotates.  The rotational version of Newton’s second law, `\Sigma \vec{\tau} = I \vec{\alpha}`, describes how the net torque about an axis through the center of mass relates to the angular acceleration of the object as it rotates.  Together, these two equations provide a complete description of how forces act to cause a rigid body to move.