Question

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

Answer

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:

Speed:
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

Search

Loading



Sponsors

USC University of Southern California Dornsife College Physics and Astronomy Department McMaster University Physics and Astronomy Department

Science Quote

'What a wonderful and amazing scheme have we here of the magnificent vastness of the Universe! So many Suns, so many Earths ...!'

Christiaan Huygens
(1629-1695)

Deal of the Day

Image of Shark Tooth Fossil in Matrix. Click on this image for more info. Shark Tooth Fossil in Matrix
Regular Price: $39.95
Today's Price: $15.00
Superb shark fossil specimen for the science classroom! Buy it now! Deal ends at midnight!

Top Selling

Here are our physics & astronomy bestsellers:
Mini Plasma Ball
Slide Making Kit
Top Secret - Spinning Top
Wood Grain Newtons Cradle
Deluxe 3D Mirascope
Solar Radiometer
Periscope
Solar Science 4M Kit
Ultimate Chemistry Set CHEM C3000
3D Magnetic Field Tube