Answer to Question #27538 in Mechanics | Relativity for hem raj

Question

A bacteria of mass 2 × 10−24 kg is rotated in a centrifuge at an angular speed of 4p × 103 rad s−1.
It is situated at a distance of 5 cm from the axis of rotation. Calculate the effective value of g
relative to the rotating frame of reference and the net centrifugal force on the bacteria.

Answer 1

Centrifugal acceleration (effective value of g) is a product of angular velocity and radius of rotation (distance to axis of rotation)
&
a = nu × r^2 = 4pi × 10^3 × 0.05^2 = 31.4 m/s^2
&
where nu is the angular speed.
The centrifugal force then is product of the mass and centrifugal acceleration:
&
F = a × m = 31.4 × 2 × 10^(-24) = 62.8 × 10^(-24) N