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Q116 (CAPF/2026) Science & Technology › Basic Science (Physics, Chemistry, Biology)

For a particle in uniform circular motion (radius R and angular velocity ω), the magnitude and direction of acceleration, respectively are

Explanation

In uniform circular motion, a particle moves along a circular path of radius R with a constant speed. Although the speed is constant, the velocity is a vector quantity that changes direction at every point. This change in direction results in an acceleration known as centripetal acceleration.

The direction of centripetal acceleration is always directed towards the centre of the circle, perpendicular to the instantaneous linear velocity. The magnitude of this acceleration is given by the formula:

a = v2/R

Given the relationship between linear velocity (v) and angular velocity (ω) is v = ωR, we substitute this into the acceleration formula:

a = (ωR)2/R = ω2R2/R = ω2R

Therefore, the magnitude is ω2R and the direction is towards the centre of the circle, making option C correct.

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