Question

A particle moves in a circle of radius R. In half the period of revolution, the displacement will be __________ and distance covered is ____________.

Answer 1

Hint: Displacement is the shortest distance between two points and distance will be the actual distance. Displacement can be negative or positive according to the direction. But distance is always a positive quantity. The distance will always be equal or more than that of the displacement.

Complete step by step answer:
Distance is the actual path covered by the body and it is a scalar quantity, whereas the displacement is the shortest distance between the initial and final point. Displacement has magnitude and direction. Distance can’t be negative or zero.
If a particle moves in a circular path of radius R, half of the revolution implies the semi-circle.

So, the distance covered by the particle will be half of the circumference of the circle.
Circumference of a circle of radius R,
\[\Rightarrow 2\pi R\]
The distance covered by the particle will be,
\[\Rightarrow \dfrac{2\pi R}{2}=\pi R\]
Since the particle covered half revolution, the displacement of the particle will be the diameter of the circle. In this diagram, the particle is going to travel in the clockwise direction. The diameter is the maximum displacement that a body can make in a circular motion. So, the particle will be at exactly opposite to the initial position. The direction will depend upon the reference point that we are considering.
\[\vec{x}=2\vec{R}\], where the vector sign implies the direction of displacement.

Additional information:
Uniform circular motion can be two types. Uniform or non-uniform circular motion with respect to the speed.
Uniform circular motion is the motion of an object travelling at a constant speed on a circular path. The period is the time required to complete one cycle of revolution.
\[T=\dfrac{2\pi R}{v}\], where v is the velocity of rotation.
In a uniform circular motion, speed will be constant but the direction will be different at each point of the circle. Frequency is the number of revolutions completed by the particle in a unit time. In a uniform circular motion, the velocity is always tangent to the path of the object. This tangent specifies the direction of motion.

Note: Displacement and distance are different quantities even if they are using the same units. Displacement will be the shortest distance between the initial and final points. Displacement is a vector quantity. In the case of circular motion, we can calculate the distance by taking the circumference of that circle. The maximum displacement in a circular motion will be the diameter.