Question

For a particle in uniform circular motion, the acceleration a at any point P(R , θ) on the circular path of radius R is (when θ is measured from the positive x -axis and v is uniform speed):

• A. $-\frac{v^2}{R}sinθi+\frac{v^2}{R}cosθj$
• B. $-\frac{v^2}{R}cosθi+\frac{v^2}{R}sinθj$
• C. $-\frac{v^2}{R}cosθi-\frac{v^2}{R}sinθj$
• D. $-\frac{v^2}{R}i-\frac{v^2}{R}j$

Answer 1

Answer: (A)

$-\frac{v^2}{R}sinθi+\frac{v^2}{R}cosθj$

Answer 2

The correct option is (C): $-\frac{v^2}{R}cosθi-\frac{v^2}{R}sinθj$.

As the particle in uniform circular motion experiences only centripetal acceleration of magnitude ω2R or

$\frac{V^2}{R}$

directed towards centre so from diagram.

$a=\frac{v^2}{R}cosθ(-i)+\frac{v^2}{R}sin(-j)$