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

Question #27538

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.

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.

Expert's answer

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

&

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

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