Question #2f31c

1 Answer
Walker P
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) #*# (2#pi# radians #/# revolution)
#alpha# = 100#pi# radians #/# minute

Or, alternatively,

#alpha# = (50 revolutions #/# minute) #*# (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.

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