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## High school physics

### Course: High school physics>Unit 7

Lesson 6: Angular momentum and angular impulse

# Angular momentum and angular impulse review

Review how both rotating objects and objects with linear momentum can have angular momentum.  Recap how torque applied to and object over a time interval can change the angular momentum of an object.

## Key terms

Term (symbol)Meaning
Angular momentum ($L$)Measure of how much rotational motion and rotational inertia an object has. Vector quantity with SI units of $\frac{\text{kg}\cdot {\text{m}}^{2}}{\text{s}}$.
Angular impulse ($\mathrm{\Delta }L$)Change in angular momentum. Vector quantity with SI units of $\frac{\text{kg}\cdot {\text{m}}^{2}}{\text{s}}$.

## Equations

EquationSymbol breakdownMeaning in words
$L=I\omega$$L$ is angular momentum, $I$ is rotational inertia, and $\omega$ is angular velocity.Angular momentum of a spinning object without linear momentum is proportional to rotational inertia and angular velocity.
$L=mv{r}_{\perp }$$L$ is angular momentum, $m$ is mass, $v$ is linear velocity, and ${r}_{\perp }$ is the perpendicular radius from a chosen axis to the mass's line of motion.Angular momentum of an object with linear momentum is proportional to mass, linear velocity, and perpendicular radius from an axis to the line of the object's motion.
$\mathrm{\Delta }L=\tau \mathrm{\Delta }t$$\mathrm{\Delta }L$ is change of angular momentum, $\tau$ is net torque, and $\mathrm{\Delta }t$ is time interval.Change in angular momentum is proportional to average net torque and the time interval the torque is applied.

## How to find the angular momentum of an object moving in a straight line

People forget that an object moving in a straight line (having linear momentum) can have angular momentum. For example, let’s say we throw a ball at one end of a stick (see Figure 1). The stick can pivot around point $O$. When the ball hits the stick, the stick rotates.
If the system of the ball and stick has no net external torque, the only way the stick could get angular momentum is from the ball during the collision. Thus, the ball must initially have some angular momentum. The ball’s angular momentum about point $O$ before the collision is
${L}_{\text{ball}}=mvr$

## Common mistakes and misconceptions

People mistakenly think any external force acting on a system will change angular momentum. Angular momentum is changed by a net external torque, but not all forces cause a torque. To produce a torque $\tau$, a force $F$ must have a lever arm $r$ and a component perpendicular to the lever arm.
$\tau =r{F}_{\perp }$
For more detail about torque, refer to our torque and equilibrium article.