What is uniform circular motion?
Uniform circular motion is the motion of an object in a circular path with constant speed.
Even though the speed is constant, the direction keeps changing at every point, so the object is actually accelerating.
Example:
- A stone tied to a string and rotated
- A car moving on a circular track
- Blades of a fan rotating
- Earth revolving around the Sun
Why is there acceleration?
In circular motion, the object keeps changing its direction of motion. This change in direction means there is an acceleration called Centripetal acceleration (acts towards the centre). Without this inward pull, the object would move in a straight line.
Derivation of speed in circular motion:
Rotating a stone
Let us take the radius of circle the stone travelled \(=\) \(r\)
Time taken for one complete revolution \(=\) \(T\)
\(Distance\ covered\ in\ one\ round\) \(=\) \(circumference \ of \ circle \) (\( 2\Pi r\))
\(Speed = \frac{Distance}{Time}\)
\(Distance=2\Pi r\)
\(Time=T\)
So,
\( v= \frac{2\Pi r}{T}\)
This formula gives the speed of an object moving in a circular path.
Illustration:
In a sporting event like hammer throw, the athlete holds the hammer in his or her hand, rotates the body in a circular motion, and then throws the hammer. The moment when the hammer is released, it goes in the same direction as it was going while releasing the hammer.
Hammer throw
Real-life example:
Motion of the moon and the earth
A satellite in a circular orbit around the earth
A cyclist on a circular track moving at a constant speed
Reference:
https://www.stockvault.net/data/2016/07/12/204199/preview16.jpg