A particle is moving in a circle of radius `R`.
a. What is its displacement when it covers (i) half the circle, (ii) full circle?
b. What is its distance when it comes (i) half the the circle and (ii) full circle ?.
.

Answer

a. (1) 2r
(2) 0
b. (1) pi*r
(2) 2pi*r

Explanation

Let `O` be the centre of a circle `r` ,.
(i) When the object completes half the circle , it moves from `A` to `B`.
Distance `= (1)/(2) xx` circumference of a circle `= (1)/(2) xx 2 pi r = pi r`
Displacement `= vec (AB) = 2 r` ( in magnitude).
(ii) when the object completes one full circle , it starts from A and comes back to `A`.
Distance = circumference of circle `= 2 pi r`
Displacement = zero , as final position coincides with the initial position.