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