Some bacteria are propelled by biological motors that spin hair-like flagella. a typical bacterial motor turning at a constant angular velocity has a radius of 1.57 x 10-8 m, and a tangential speed at the rim of 2.21 x 10-5 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?

(a)

(b)

Explanation:

The angular speed is a measure of the rotation speed. Thus, It is defined as the angle rotated by a unit of time:

The arc length in a circle is given by:

s is the length of an arc of the circle, so .

Replacing (2) in (1):

a) Now, we calculate the angular speed:

b) We use (1) to calculate the time it takes to make one revolution, which means that is .

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