Question

Some bacteria are propelled by motors that spin hair-like flagella. A typical bacterial motor turning at a constant angular velocity has a radius of 1.3 x10-8m, and a tangential speed at the rim of 2.1 x10-5 m/s. (a) What is the angular speed (the magnitude of the angular velocity) of this bacterial motor? (b) How long does it take the motor to make one revolution?

Answer 1

Answer :

(a) The angular speed of this bacterial motor is $1.6\times 10^3s^{-1}$

(b) The time taken by the motor to make one revolution is $3.9\times 10^{-3}s$

Explanation :

(a) To determine the angular speed of this bacterial motor.

Angular speed : It is defined as the rate at which an object changes its angle.

Formula used :

$\omega=\frac{v}{r}$

where,

$\omega$ = angular speed

v = tangential speed = $2.1\times 10^{-5}m/s$

r = radius = $1.3\times 10^{-8}m$

Now put all the given values in the above formula, we get:

$\omega=\frac{2.1\times 10^{-5}m/s}{1.3\times 10^{-8}m}$

$\omega=1.6\times 10^3s^{-1}$

Thus, the angular speed of this bacterial motor is $1.6\times 10^3s^{-1}$

(b) to determine the time taken by the motor to make one revolution.

Formula used :

$T=\frac{2\pi}{\omega}$

where,

T = time

Now put all the given values in this formula, we get:

$T=\frac{2\times 3.14}{1.6\times 10^3s^{-1}}$

$T=3.9\times 10^{-3}s$

Thus, the time taken by the motor to make one revolution is $3.9\times 10^{-3}s$