Random Math Stuff (WARNING: Imminent Brain Pain)

Ever wonder if a spinning disc has the same velocity all throughout its surface? Of course you don't! Nonetheless, I can prove that a point closer to the center of a disc spins slower than a point farther from the center. I'll do this with what I like to call the vinyl record example.

Let's say a 16" record is spinning at 120 rpm (or 2 rps). What's the difference between a point 3 inches from the center of the record (a) and a point 8 inches from the center (b)?

First, you need to find the circumferences of each point's path.

C(a) = (3 * 2)π inches = 6π inches
C(b) = (8 * 2)π inches = 16π inches

Next, you need to find the distance each point travels every minute.

6π * 120 = 720π inches
16π * 120 = 1920π inches

Then, you need to determine the speed each point is traveling.

S(a) = 720π inches / 60 seconds = approx. 37.69911184307752 inches per second
S(b) = 1920π inches / 60 seconds = approx. 100.5309649148734 inches per second

Finally, you need to convert the units from ips to mph.

S(a) = approx. 37.69911184307752 ips = approx. 2.14199499 mph
S(b) = approx. 100.5309649148734 ips = approx. 5.71198659 mph

The difference between both speeds is approximately 3.5291916 mph. In case you were wondering, no. A point between those points doesn't travel at that speed; it travels at approximately 2.85599332 mph.

Why did I do this, you may ask? Well, because I have nothing better to do with my life. Now, if you'll excuse me, I'm gonna go ahead and ponder it.