Question

A particle is moving around a circular path with uniform angular speed $\left(\omega \right)$. The radius of the circular path is (r). The acceleration of the particle is?

• A. $\frac{{\omega }^2}{r}$
• B. $\frac{\omega }{r}$
• C. $v\omega$
• D. vr

Answer 1

The correct option is A $\frac{{\omega }^2}{r}$

when a body is revolving around a circular path, it experiences 2 forces: Centrifugal force and Centripetal Force.

Centrifugal force describes the tendency of an object following a curved path to fly outwards, away from the center of the curve. It's not really a force; it results from inertia, the tendency of an object to resist any change in its state of rest or motion.

Centripetal force is a real force that counteracts the centrifugal force and prevents the object from "flying out," keeping it moving instead with uniform speed along a circular path.

Centripetal force: $Fc=\frac{m{v}^2}{r}=\frac{{\omega }^2}{r}$

Thus acceleration of particle in radial direction is equal to w2r where w is the angular velocity of particle and r is the radius of the circular path.