- #1

brochesspro

- 155

- 22

**Relevant formulae:-**

Angular velocity in uniform circular motion ##=## ##\omega## ##=## ##\frac {2\pi} t##, where ##t## is the time taken to complete one revolution.

Centripetal acceleration in uniform circular motion ##=## ##a## ##=## ##\omega^2r##, where ##r## is the radius of the circular path.

I solved both the problems. I plotted the graph in GeoGebra and obtained the following.

It looks cool, even if I do say so myself.

Note that I took the natural logarithm of the obtained results, and I converted the quantities to their SI counterparts and plotted the graph.

##ln(r)## is on the X axis where ##r## is in m, and ##ln(a)## is on the Y axis where ##a## is in ms

^{-2}. A distance of 1 on the graph equals 1 unit.

My question is, why does this happen. Why do we get a straight line on joining the points? Could someone please explain how this wonderful phenomenon occurs? I could give you any other data you may require about how I made this graph. Thank you.

P.S. The book from where this problem is taken:-

Ohanian, Hans C.

*Physics.*Vol. 1. 2nd ed., expanded. New York, NY: Norton, 1989. ISBN: 9780393957501.

http://www.amazon.com/exec/obidos/ASIN/0393957500/ref=nosim/mitopencourse-20

Latest edition:-

Ohanian, Hans C., and John T. Markert.

*Physics for Engineers and Scientists*. Vol. 1. 3rd ed. New York, NY: Norton, 2007. ISBN: 9780393930030.

http://www.amazon.com/exec/obidos/ASIN/0393930033/ref=nosim/mitopencourse-20