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