Thomas R. answered • 04/22/18

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Over 25 years of experience and a sense of humor about math

You can perform the steps in a few different orders, but they will all lead to the same place in the end. Here's the sequence I think you will find easiest:

First, the question asked for revolutions per minute, not second. Let's turn everything into minutes.

I assumed you meant 3π

2

for the angle, and not 3 , am I right? That gives you the complex fraction

2π

3πrad/2 Let's rewrite that as:

1 second

3π rad x 60 sec because dividing 3/2 by 1 is just 3/2, letting us reduce that complex fraction. You get

2 sec 1 minute

90π rad after cancelling the word "second" and reducing the 2 with 60.

1 minute

Now, the sneaky but easy part. You complete 1 revolution for every 2π radians of spin, so we multiply two more fractions:

1 rev x 90π rad Cancelling the word "radian" as well as reducing the π, the 2 and the 90 yields

2π rad 1 minute

45 rev Your book might also write it as "45 rpm".

1 minute