Angular Acceleration

### Guidance

You may already be familiar with the measurement of acceleration as the relationship of an object's changing velocity to the time it has been in motion. However, this relationship is for objects that are moving in a straight line. What about objects that are traveling on a circular path?

Do you remember biking down a steep hill when you were younger?

A would go faster and faster down the hill, your linear velocity was increasing.  When your linear velocity changes we call that acceleration. But what about your tires, they spin faster and faster, their rotational (angular) velocity is increasing.  When your rotational velocity changes, in this case increasing, we call that rotational acceleration.

Imagine the point on the larger circle is the person on the edge of the merry-go-round and the point on the smaller circle is the person towards the middle. If the merry-go-round spins exactly once, then both individuals will also make one complete revolution in the same amount of time.

The formula for angular acceleration is:

is the first letter in the Greek alphabet, alpha, and is commonly used as the symbol for angular acceleration. is the angular velocity of rotation expressed in radian per sec measure, and $t$ is the time of its rotational motion.

#### Example A

When a bowling ball is first released it slides down the alley before it starts rolling.  If it takes 1.2 seconds for a bowling ball to attain an angular velocity of 6 rev/sec, determine the average angular acceleration of the bowling

Solution: