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 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 = omega R = 0.44 s^(-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 directe 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 cm s^(-2)`