An object of mass m moves with a uniform speed v round a circular path of radius r. If its angular speed is \(\omega\), the magnitude of the centripetal for...

An object of mass m moves with a uniform speed v round a circular path of radius r. If its angular speed is \(\omega\), the magnitude of the centripetal force acting on it is

Answer Details

When an object of mass m moves in a circular path of radius r with uniform speed v, it experiences a force towards the center of the circle known as the centripetal force. The magnitude of the centripetal force is given by the formula F = ma, where a is the centripetal acceleration. The centripetal acceleration can be expressed in terms of the angular speed \(\omega\), as a = r\(\omega^2\). Therefore, the magnitude of the centripetal force can be calculated by multiplying the mass of the object by the centripetal acceleration. So, F = ma = m(r\(\omega^2\)) = m\(\omega^2\)r Hence, the correct option is: - \(m \omega^2 r\)