Write the equations for centripetal acceleration and centripetal force for uniform circular motion.

(N/A) For an object of mass $m$ moving in a circular path of radius $r$ with a constant speed $v$ (or angular velocity $\omega$),the equations are as follows:
$1$. Centripetal Acceleration $(a_c)$: The acceleration directed towards the center of the circular path is given by:
$a_c = \frac{v^2}{r} = r\omega^2$
$2$. Centripetal Force $(F_c)$: According to Newton's second law $(F = ma)$,the force required to maintain uniform circular motion is:
$F_c = m a_c = \frac{mv^2}{r} = mr\omega^2$
Here,$v$ is the linear speed,$r$ is the radius of the circular path,$m$ is the mass of the object,and $\omega$ is the angular velocity.