# Question #2f31c

Feb 25, 2016

Recall:
The term velocity is really just going to refer to something's positing as a function of time. So an angular velocity is just measuring how much its angle is changing over time.

#### Explanation:

If the object is going around in a circle, ("swung around" implies that it is attached to a rope of some kind going in a circle), it will pass through 360 degrees, or 2$\pi$ radians per rotation.

If it is swung around 50 times in 1 minute, its angular velocity can be calculated as:

$\alpha$ = (50 revolutions $/$ minute) $\cdot$ (2$\pi$ radians $/$ revolution)
$\alpha$ = 100$\pi$ radians $/$ minute

Or, alternatively,

$\alpha$ = (50 revolutions $/$ minute) $\cdot$ (360 degrees $/$ revolution)
$\alpha$ = 18,000 degrees $/$ minute

Note that the mass given in this problem is irrelevant. Just because something has a different mass will not change how fast its angle is changing.