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 isits magnitude ?

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

1.	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 isits magnitude ?
Answer» Solution :This is a example of uniform circular MOTION . HereR= 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 directedtowards 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)`