Question

A ball is moving in a circle of radius `3m`. At a certain instant its angular speed is `2rad//s` and the angular speed is increasing at `3rad//s^(2)`. Find the tangential and centripetal components of the acceleration of the ball and magnitude of acceleration.

Answer 1

`a_(t)=ralpha=3xx3=9m//s^(2)`
`a_(c)=omega^(2)r`
`=(2)^(2)xx3=12m//s^(2)`
`a=sqrt(a_(c)^(2)+a_(t)^(2))`
`=sqrt((12)^(2)+(9)^(2))=15m//s^(2)`