A rotating fan completes 1200 revolutions every minute. Consider a point on the tip of the blade,...?

Question

at a radius of .15m. (A) Through what distance does the point move in one revolution. (B) What is the speed of the point? (C) What is its acceleration?

Answer 1

Okay, either you're not thinking at all, or you are thinking too hard.

Let's back up.  Let's say I had a circle, with radius r.  What would the distance around the circle (circumference) be?  That is the answer for part A.  (just substitute 0.15m in for r).

Now, let's call that circumference C.  It is a distance, equal to one revolution.  So if C = 2 meter, then each revolution is 2 meter.  1200 revolutions per minute becomes 2*1200 = 2400 meters/minute.  Hopefully you get the point.  The way you can think of this is "dimensional analysis" -- you can multiply and divide by the same number (just in different units).

So 1200 revolutions/minute * 2 meters/revolution  * 1minute/60seconds

gives you the answer in meters per second.  1 minute = 60 seconds, so you can multiply by 1 minute (to cancel the minutes in the denominator), and then divide by 60 seconds.

(again, I just used 2 meters as an example.. use the actual circumference).

Finally, for acceleration of a rotating body, you should see in your textbook or lecture notes an equation for centripetal acceleration.  It looks something like a = v^2 / r.  So, you found v in part B, and r was given to you.  Note that if you left the units in meters/minute, then you would have meters/minute^2, but if you change velocity to meters/second, then you get meters/sec^2.