An insect trapped in a circular groove of radius `12 cm` moves along the groove steadily and completes ` 7` revolutions in `100 s.` (a) What is the angular speed , and the linear speed of the motion ? (b) Is the acceleration vector a constant vector ? What is its magnitude?

Explanation

Her, `T =100//7 s, r =12 cm `
(a) Angular speed , ` omega= (2 pi)/T =(2 xx (22//7)/((100//7))` ltbrltgt `=0.44 rad//s`
Linear speed, `v =r omega 12 xx 0.44`
`=5.3 cm s^(-1)`
(b) The given motion is a uniform circular motion. Here the direction of velocity id along the tangent to the circle at every point. The acceleration in this motion is centripetal acceleration. It is alwys directed towards the centre of the circle. Since this direction changes therfore, the acceleration here is not a constant vector. The magnitude of acceleration is `
`_(c) =omega ^(2) =(0.44 )^(2) xx 12 2.3 cm s^(2)`.