Torque and Rotational Motion

Torque and rotational motion extend the principles of Newtonian mechanics from linear (translational) motion to objects that rotate about an axis. Just as a net force causes linear acceleration, a net torque causes angular acceleration. Every concept from linear mechanics has a rotational analog: force becomes torque, mass becomes moment of inertia, linear velocity becomes angular velocity, and momentum becomes angular momentum. Mastering these parallels is the key to solving rotational problems efficiently.

Torque is the rotational equivalent of force, defined as the cross product of the lever arm and the applied force: tau = r x F, with magnitude tau = rF sin(theta). The moment of inertia (I) is the rotational equivalent of mass, representing an object's resistance to angular acceleration. Unlike mass, moment of inertia depends on how mass is distributed relative to the axis of rotation. Newton's second law for rotation states that the net torque equals the moment of inertia times the angular acceleration: tau_net = I * alpha. Rotational kinetic energy is (1/2)I * omega^2, and the total kinetic energy of a rolling object includes both translational and rotational components.

Angular momentum (L = I * omega) is conserved when no external torque acts on a system, leading to some of the most dramatic demonstrations in physics: figure skaters spinning faster when they pull in their arms, collapsing stars becoming pulsars, and gyroscopes maintaining their orientation in space. AP Physics 1 requires students to solve problems involving static equilibrium (net force and net torque both zero), rotational dynamics (applying tau = I * alpha), conservation of angular momentum, and rolling motion. The ability to draw extended free-body diagrams showing where forces act and compute torques about strategic pivot points is essential.

Practice a little. See where you stand.