The angular speed of the rotor in a centrifuge increases from 420 to 1420 rad/s in a time of 5.00 s. (a) Obtain the angle through which the rotor turns. (b) What is the magnitude of the angular acceleration?

Explanation:

Using the circular equations of motion,

dw = dθ/dt

θ = (wi - wo)*t/2

Where,

θ = angular displacement

wi = final angular velocity

= 1420 rad/s

wo = initial angular velocity

= 420 rad/s

t = time

= 5s

θ = (1420 - 420)*5/2

= 2500 rad.

2*pi rad = 1 rev

= 397.89 rev

wi = wo + αt

Where,

α = angular accelaration

1420 = 420 + 5α

α = 1000/5

= 200 rad/s^2.

b. a lightning bug, plug of grass, and a worm