Question

A particle moves in a horizontal circle of radius r. The angular velocity of particle veries at a constant rate α. The acceleration of the particle is

(1) v² / r

(2) rα

(3) v²/r + rα

(4) \([(\frac{v^2}{r})^2+(rα)^2]^{1/9}\)

Answer 1

 (4) \([(\frac{v^2}{r})^2+(rα)^2]^{1/9}\)

The acceleration has two components.

(a) The radial component of acceleration is due to change direction of the velocity and equals v²/r.

(b) The tangential component is due to change in magnitude of v and equals rα.

The two component of acceleration are mutually perpendicuular. The net acceleration is

 a = \([(\frac{v^2}{r})^2+(rα)^2]^{1/2}\)