Question

if the angular speed doubles, then the number of revolution doubles. answer is yes but pls justify with examples

Answer 1

A revolution is just an angle of 2pi. Revolutions per unit of time is a measure of angular speed.

Answer 2

\(\large \rm Angular ~speed= ω =\frac{dθ}{dt}=\frac{number~of~revolutions}{time~taken}\)

\(\large \rm Angular ~speed=\frac{number~of~revolutions}{time~taken}\)

\(\large \rm ↑Angular ~speed=\frac{↑number~of~revolutions}{time~taken}\)

For examples, you can consider a horizontal circular motion of a rigid mass attached to an inextensible string. As the tension in the string is increased, the angular velocity is also increased, increasing the number of revolutions.

You can also consider the circular motion of a compact disk, or even a wheel of a vehicle.

Note:- In your question, remember the time remains constant before and after doubling the angular speed.

Answer 3

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if the angular speed doubles, then the number of revolution doubles.
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that is incomplete: the number of revolutions doubles *in the same amount of time*

but with that said, it is almost by definition: angular speed is number of revolutions per unit time, so doubling it means double the number of revolutions that occur in that same unit time.