# Linear and Angular Velocity in Circular Motion

- Author:
- Ken Schwartz

Click the "Animate" box. The two red dots move around their circles at the same rate. Now use the a or b slider to change the size of one of the circles. What do you notice about the speed of the red dots? Which one appears to be moving faster? Which one completes one trip around the circle first?
Even though the red dot on the larger circle is moving faster, it takes the same time to complete one revolution around the circle. This illustrates the concepts of linear velocity (speed along the circumference) and angular velocity (speed of revolution). Although these quantities are closely interrelated, they each have their own purpose.

The

*angular velocity*of the two red dots always remains the same. We measure angular velocity as the amount of rotation in a period of time. Commonly-used units for angular velocity include revolutions per minute (RPM, how many trips around the circle in one minute) and radians per second (rad/s, how many radians of angle are swept in one second). Both of these quantities measure the speed of rotation. The*linear velocity*of the two dots can be made to be very different from each other by changing the radius of one or both circles. Linear velocity measures how fast the dot is moving along the circumference of the circle. It's called "linear velocity" because we use linear measurements like meters or miles to mesaure circumference. The larger the radius, the farther the dot has to go in one period of time, so the faster it must move along the cirrcumference.