Question

Define angular velocity. Show that the centripetal force on a particle undergoing uniform circular motion is -mw^2r

Answer 1

Answer:

The rate of change of angular position of rotating body.

Explanation:

Angular velocity applies to those objects that moves along a circular path. Angular velocity is measured in radian/second or angle/seconds. Similarly the rate of change of angular velocity is angular acceleration.

Now we know that if an object is moving in a circular path with constant speed still its velocity will be changing as its direction is changing at every point. It means that it is accelerating and it is inward acceleration. This inward acceleration is called centripetal acceleration.

a(c)= V^2/r where V is the magnitude of velocity and r is the radius of the circular path of motion.

ω represents angular velocity and is linked with linear speed with the formula;

V=rω.

centripetal acceleration will now be ---(ωr)^2/r

a(c)=rω

we know the F =ma

centripetal force, therefore is equal to m into a(c) ----- mrω(^2).