Question

An object is in uniform circular motion, tracing an angel at 30 degrees every 0.010 seconds. What's the period of this motion and how do I work it out?

Answer 1

Here's the rule you need to know
in order to answer this question:

                     1 full circle ==> 360 degrees .

Got that ?

Now you could set up a proportion:

     (30 degrees) / (0.01 second)  =  (360 degrees) / (time for full period)

Cross-multiply the proportion:

     (30°) · (period)  =  (360°) · (0.01 sec)

Divide each side by (30°) :    Period = (360° · 0.01 sec) / (30°)

                                                     =  (3.6° · sec) / (30°)

                                                     =  (3.6 / 30)  sec

                                                     =      0.12  sec .
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Another way to look at it:

30°        takes    0.01 second
60°        takes    0.02 second
90°        takes    0.03 second
120°      takes    0.04 second
150°      takes    0.05 second
180°      takes    0.06 second
210°      takes    0.07 second
240°      takes    0.08 second
270°      takes    0.09 second
300°      takes    0.10 second
330°      takes    0.11 second
360°      takes   0.12 second