Question 576243
<pre>
Each rotation is 360° so 45rpm = 45×360° rotations/minute

We convert 45 revolutions/minute to degrees/second

We begin with this fraction:

{{{45rev/(min)}}}

Each revolution is 360 degrees, so we multiply by this unit fraction {{{360deg/(1rev)}}}.  So we have:

{{{45rev/min}}}×{{{360deg/(1rev)}}}  

Each minute is 60 seconds so we multiply by the unit fraction {{{1min/(60sec)}}}

{{{45rev/min}}}×{{{(360deg)/(1rev)}}}×{{{(1min)/(60sec)}}}

We cancel the rev's and the min's

{{{45cross(rev)/cross(min)}}}×{{{360deg/(1cross(rev))}}}×{{{1cross(min)/(60sec)}}}

{{{expr(45*360/60)}}}{{{deg/(sec)}}}

That comes out to 

270 degrees per second.

So 270 seconds at 270 degrees per second is a rotation through 270×270
or 72900 degrees.

Edwin</pre>