If I am on a merry-go-round with a friend, and the friend is closer to center than I am, are they going faster then I am?
Asked by: Nunya


No, you are going faster. The merry-go-round is rotating with uniform circular motion - that means that it rotates at a constant angular speed.

Now lets say your friend is a distance r from the centre which is also equal to the radius of her circular path and you are a distance R.

Distance travelled in one period:
Friend = 2*pi*r
You = 2*pi*R
which is the circumference of your respective circular paths.

Lets say that the time period of one complete circle is T:

Friend= 2*pi*r/T
You= 2*pi*R/T

Now by the definition of angular speed
w=2*pi/T where w is the angular speed in radians/s

So this means that the speed is:
Friend= rw
You= Rw

Since you are circling with uniform circular motion w is the same for both of you meaning that the closer you are to the centre the slower your linear speed is.
Answered by: Martin Archer, Physics student, Imperial College London, Uk
xUmp Science eStore

Science Quote

J. Robert Oppenheimer Photo

'The atomic bomb ... made the prospect of future war unendurable. It has led us up those last few steps to the mountain pass; and beyond there is different country.'

J. Robert Oppenheimer

- All rights reserved. © Copyright '1995-'2018