# How does angular momentum differ from linear momentum?

May 7, 2018

The major conceptual difference is that one object's motion is linear and the other object's motion is rotational.

#### Explanation:

Both types of momentum are a measure of the object's tendency to continue moving in the way it is moving. Momentum is conserved in both linear and angular.

But there are practical differences that affect your calculations.

• Momentum Equation
Linear: $p = m \cdot v \text{ }$
Angular: $L = I \cdot \omega$
• Variables Related to Inertia -- $m \text{ vs. } I$
Linear: $\text{mass, m}$ with units of kg "
Angular: $\text{Rotational Inertia} , I$ with units of $k g \cdot {m}^{2}$
• Variables Related to Velocity -- $v \text{ vs. " omega}$
Linear: $v$ has units of $\frac{m}{s}$ (equivalent units are acceptable in certain cases)
Angular: $\omega$ has units of $\frac{\text{radians}}{s}$ (equivalent units are acceptable in certain cases)

Special notes about $\text{Rotational Inertia}$:
There are formulae for various geometric shapes and various locations of axis of rotation. For example, for a solid sphere rotating about a diameter use $I = \frac{2 \cdot m \cdot {r}^{2}}{5}$. These differences give mass that is farther from the axis of rotation more effect.

I hope this helps,
Steve