Conservation of Angular Momentum - AP Physics 1

Angular velocity. Rate of rotation measured in radians per second.

No effect; moment of inertia is mass and shape dependent. Moment of inertia depends only on mass distribution.

Total angular momentum remains constant if no external torque acts. Fundamental principle when no external torques act on system.

A measure of the force that can cause an object to rotate about an axis. Rotational analog of force for linear motion.

$L = 4 \text{ kg} \cdot \text{m}^2/\text{s}$. $L = mvr = 2 \times 4 \times 0.5 = 4$ units.

$L = I\omega$. For rigid bodies: moment of inertia times angular velocity.

Angular momentum changes. External torque causes rate of change in angular momentum.

$L = mvr \sin \theta$. For point mass: momentum times radius times sine of angle.

Angular velocity quadruples. Since $I = mr^2$, halving $r$ quarters $I$, so $\omega$ quadruples.

Angular velocity decreases. Since $L = I\omega$, larger $I$ requires smaller $\omega$.

Kilogram meter squared per second ($\text{kg} \cdot \text{m}^2/\text{s}$). Derived from $L = mvr$ with standard SI base units.

No net external torque. Zero net torque is required for conservation.

Angular velocity increases. Since $L = I\omega = mr^2\omega$, smaller $r$ requires larger $\omega$.

Friction can reduce angular momentum by exerting external torque. Creates external torque that opposes rotational motion.

$\tau = \frac{dL}{dt}$. Torque equals the time rate of change of angular momentum.

It can change the system's angular momentum. External forces can create torques that change $L$.

$\omega$. Greek omega represents angular velocity in physics.

$I = mr^2$. Mass times distance squared from rotation axis.

$I = \frac{1}{3}mL^2$. Standard formula for rod rotating about one end.

Moment of inertia. Rotational inertia - resistance to angular acceleration.

Remains constant. Conservation applies - only $I$ and $\omega$ change, not $L$.

Angular momentum is the rotational analog of linear momentum. Both describe inertial motion in their respective domains.

Angular velocity. Rate of rotation measured in radians per second.

Angular velocity increases as the star's radius decreases. Conservation requires $\omega$ to increase as radius shrinks.

Its moment of inertia changes. Redistributing mass changes the moment of inertia $I$.

Stability increases. Larger $I$ resists changes in rotational motion.

Angular momentum doubles. Since $L = I\omega$ and $I = mr^2$, doubling $m$ doubles $L$.

$\Delta L = \tau t$. Impulse-momentum theorem applied to rotational motion.

$\tau = rF \sin \theta$. Force times lever arm times sine of angle between them.