Question

An insect trapped in a circular groove of radius 12 cm moves along the groove steadily and completes 7 revolutions in 100 s. (i) What is the angular speed and the linear speed of the motion ? (ii) Is the acceleration vector a constant vector ? What is its magnitude ?

Answer 1

This is an example of uniform circular motion. Here, R=12cm. The angular speed omega is given by
`omega=2pi//T = 2pixx7//100 = 0.44 rad//s`
The linear speed v is:
v=`omegaR = 0.44 s^(-1) xx 12`cm =`5.3 cms^(-1))`
The direction of velocity v is along the tangent to the circle at every point. The accleration is directed towards the center 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)`
`2.3cm s^(-2)`