Moment of inertia for a hoop is a measure of its resistance to angular acceleration. The polar moment of inertia formula, J = mr², relates the hoop’s mass (m) and radius (r) to its moment of inertia. As a hoop rotates, its angular momentum depends on its moment of inertia. The inertia tensor provides a complete description of the hoop’s resistance to rotation. Torque applied to the hoop results in angular acceleration and changes in angular velocity. The relationship between angular velocity and kinetic energy highlights the significance of moment of inertia in understanding the dynamics of rotating hoops.
