Athlete running on a hexagonal track
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The figure shows an athlete running with uniform speed on a track which has a shape of a regular hexagon.
The athlete runs with uniform speed along the segments AB, BC, CD, DE, EF and FA of the track and at the turns he quickly changes his direction of motion to stay on the track, without changing his speed. Similarly if the track was a regular octagon the athlete would have changed the direction of motion eight times to remain on the track. As the number of sides of the track increases, the athlete has to turn more often. Now if we increase the number of sides indefinitely the shape of the track will approach the shape of a circle. Therefore a circle can be considered as a polygon with infinite sides and hence motion along a circular path is classified as non-uniform motion.
Thus, an object moving along a circular track with uniform speed is an example for an accelerated motion because the direction of motion of the object goes on changing at every instant of time.
Differences between uniform linear motion and uniform circular motion
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| Uniform Linear Motion | Uniform Circular Motion |
|---|
| The direction of motion is fixed | The direction of the motion changes continuously with time |
| It is not an example of accelerated motion | It is an example of accelerated motion |
Examples of uniform circular motion
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1) A car negotiating a curve with uniform speed.
Car negotiating a curve
2) Whirling a hammer in a circle by an athlete before throwing it.
An athlete whirling a hammer
3) An aircraft moving in a loop.
Aircraft moving in a loop
Suppose an athlete takes t seconds to go once around the circular path of radius r, then the velocity v is given by the relation
V = $\frac{distance travelled}{time}$
distance traveled = circumference of the circle
= 2 pi r
Linear velocity = 2 Π r / t
