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

Answer on Question #40679, Physics, Mechanics | Kinematics | Dynamics

Question:

A bacteria of mass $2 \times 10^{-24} \, \mathrm{kg}$ is rotated in a centrifuge at an angular speed of $4p \times 103$ rad s$^{-1}$. It is situated at a distance of $5 \, \mathrm{cm}$ 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:

Centrifugal acceleration (effective value of $g$) equals:

$$a = \omega^{2} r = 7.9 \cdot 10^{6} \frac{m}{s^{2}}$$

where $\omega$ is angular speed, $r$ is distance from the axis of rotation.

Net centrifugal force on the bacteria equals:

$$F = m a = 1.6 \cdot 10^{-17} \, N$$

where $m$ is mass, $a$ is acceleration

Answer: $a = 7.9 \cdot 10^{6} \frac{m}{s^{2}}, F = 1.6 \cdot 10^{-17} \, N$