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Matthew Hutchins' Physics of A Merry-Go-Round
Linear Speed
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In circular speed a term that comes up a lot is uniform circular motion.  Basically this means that an object is traveling in a perfect circle at a constant speed.  Notice how I said speed NOT velocity.  That is because as I said earlier velocity is a vector meaning it would have to remain at the same speed and continue in the same direction.  Since it is traveling in a circle it is constantly changing direction thus changing its velocity.

 

The basic velocity formula can be used to determin the average velocity that an object is traveling in a circle.

 

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The circumference can be found using the formula

 

Circumference = 2*pi*radius

Combining these formulas will give us a new on that can be used but the time will be the time for the object to make one complete revolution around the circle (period)

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If you analyze this formula you can see that that larger the radius the higher the speed will be.  So if you are on a merry-go-round and you were to walk from the center towards the outside your speed would increase as you walk out.  An easy experiment can be done to show this.  If you were to attach four LED lights to a string and then spin them in a circle it can be seen that the light on the outside is spinning at a faster rate than that of the light closest to the center.

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Since the lights are attached to the same string and the same force is being applied to spin all the lights the lights on the outside need to spin faster in order to cover the same amount of distance.
 

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As I said earlier that you don’t have a constant velocity in uniform circular motion.  The velocity vector is always tangent to the circle at any point on the circle.  This and the concept of inertia shows why on a merry-go-round your body wants to fly off.  If you were to have an aerial view of someone letting go of the bar on a merry-go-round you would see them fly off tangent to the point at which they let go.

Continue to ANGULAR SPEED

İMatthew Hutchins 2004