How many revolutions will a turntable that rotates through an angle of 3 over 2 pi in one second make in 60 seconds?

How many revolutions will a turntable that rotates through an angle of 3 over 2 pi in one second make in 60 seconds?
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Answer :

I guess you mean 3 pi over 2, ie 3π/2 though it may have been given to you as (3/2)π To solve this, find the total angle turned in 60 seconds and divide by the angle in a whole turn, ie one revolution. In 60 seconds it will turn through an angle of 60 × 3π/2 radians = 90π radians One revolution is 2π radians → 90π radians = 90π/2π revolutions = 45 revolutions (45 rpm - the figure calculated - was the standard for a single).
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