If wheel turning at a constant rate completes 100 revolutions in 10 s its angular speed is:

The guy above did it in a weird way. To keep it simple, one revolution is 2pi.

Angular speed is revolutions over time -- but it really depends on the units. For example, in the problem, its rads/sec. So we have to mult. the revs by 2pi (for radians). If it was just revs/sec, you would just divide 100/10.

Anyway, so now all we have to do is multiply 100 by 2pi and divide it by the time. Keep in mind of the units, because doing this will get this rads/sec. You can always convert it though:

1 Rev = 2pi - we use this to convert

--> 100rev(2pi) / 10s = 62.831 rads/s

You can also think of it like this :

Angular speed (in rads/time) = Revolutions*2pi / time

[assuming 2pi isnt accounted for in the revolutions]

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