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Session Length
~17 min
Adaptive Checks
15 questions
Transfer Probes
8
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.
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The rotational equivalent of force. Torque equals the lever arm times the component of force perpendicular to the lever arm: tau = rF sin(theta). It causes angular acceleration around an axis of rotation. Measured in newton-meters (N*m).
Example: Pushing a door at its handle (far from the hinge) requires less force than pushing near the hinge because the longer lever arm produces greater torque for the same force.
The rotational equivalent of mass — a measure of an object's resistance to angular acceleration. It depends on both the mass and how that mass is distributed relative to the axis of rotation: I = sum(m_i * r_i^2).
Example: A hollow cylinder has a greater moment of inertia than a solid cylinder of the same mass and radius because more mass is concentrated far from the axis.
The rotational equivalent of linear momentum, defined as L = I * omega for a rigid body rotating about a fixed axis. Angular momentum is conserved when no net external torque acts on the system.
Example: A figure skater pulls in her arms (reducing I) and spins faster (increasing omega) to conserve angular momentum during a spin.
The net torque on an object equals its moment of inertia times its angular acceleration: tau_net = I * alpha. This is the rotational analog of F_net = ma.
Example: A heavier merry-go-round (larger I) requires more torque to achieve the same angular acceleration as a lighter one.
The kinetic energy of a rotating object: KE_rot = (1/2)I * omega^2. For rolling objects, total KE = (1/2)mv^2 + (1/2)I * omega^2 (translational + rotational).
Example: A bowling ball rolling down a lane has both translational kinetic energy (from moving forward) and rotational kinetic energy (from spinning), so it moves slower than a frictionless sliding block.
A condition where both the net force and the net torque on an object are zero, so the object is neither accelerating linearly nor angularly. Essential for analyzing beams, ladders, and bridges.
Example: A seesaw balances when the clockwise torque from one child equals the counterclockwise torque from the other: m1 * g * r1 = m2 * g * r2.
A condition where the contact point between a rolling object and the surface has zero velocity. The translational speed v and angular speed omega are related by v = R * omega.
Example: A bicycle tire rolling on pavement without skidding satisfies v = R * omega. The speedometer reading (from wheel rotation) accurately reflects the bike's speed.
Angular velocity (omega) is the rate of change of angular position, measured in rad/s. Angular acceleration (alpha) is the rate of change of angular velocity, measured in rad/s^2.
Example: A spinning top that completes one full rotation (2*pi radians) in 0.5 seconds has an angular velocity of 4*pi rad/s (approximately 12.6 rad/s).
More terms are available in the glossary.
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