An insect trapped in a circular groove of radius 12 cm moves along the groov 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

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)`