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 ?

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 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 ?
Answer» Solution :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 : `upsilon = 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 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 cm s^(-2)`