An insect trapped in a circular groove of radius 12 cm moves along the groove steadily and completes7 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 Us magnitude ?

Explanation

This is an example of uniform circular motion.
Here, R =12 cm. The angular speed `omega` is
Given by
`omega = 2pi//T =2pi xx 7//100 = 0.44` rad/s
The linear speed v is:
`v=omegaR =0.44S^(-1) xx 12 cm = 5.3 cm S^(-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 =(0.44 S^(-1))^(2) (12 cm) = 2.3 cms^(-2)`