An insect trapped in a circular groove of radius `12 cm` moves along the groove steadily and commpletes ` 7` revoltions in `100 s.` (a) What is the angulr speed , and thelinear speed of the motion ? (b) Is the acceleration vector a costant vector ? What is its magnitude?

Explanation

This is a example of uniform circular motion . Here R= 12 cm . The angular speed `omega` is given by
`omega=2pi//T=2pixx7//100=0.44 " red "//s`
The linear speed v is :
`v=omegaR0.44s^(-1)xx12cm=5.3cms^(-1)`
The direction of velocity v is along the tangent to the circle at every point . The acceleration is directed towards the centre of the circle . Since this direction changes continuously, acceleration here is not a constant vector . However , the magnitude of acceleration is constant :
`a=omega^(2)R=(0.44s^(-1))^(2)(12cm)`
`=2.3 " cm "s^(-2)`