Question

Define uniform circular motion. A particle is travelling in a circle of diameter \[15m\]. Calculate the distance covered and the displacement when it completes two rounds.

Answer 1

Hint: uniform circular motion is a type of circular motion in which a particle moves in a circle with fixed speed or type of motion in a circle in which angular velocity is constant throughout the motion.

Complete step by step answer:
For uniform circular motion speed of particle rotating in the circle remains fixed and it is defined as-
If movement of an object along the circumference of the circle is with constant speed then it is called uniform circular motion
In uniform circular motion only speed remains fixed but velocity of the particle keeps changing because at every instant direction of motion of particle changes and centripetal acceleration (which is acceleration of the particle moving in circle towards centre ) is provided by centripetal force.
When a particle moves in a circular motion and it completes 2 rounds then
Distance travelled $d = 2 \times 2\pi r$
Putting value of r we have $d = 2 \times 2 \times 3.14 \times 15 = 188.4m$
And displacement will be zero as initial and final positions are the same.

Note:
For uniform circular motion only speed remains fixed but velocity keeps changing as direction at each instant keeps changing and due to changing of this velocity a centripetal acceleration exists which is provided by centripetal force.