Question

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 1.61 10-8 m, and a tangential speed at the rim of 2.33 10-5 m/s. (a) What is the angular speed (the magnitude of the angular velocity) of this bacterial motor?

Answer 1

Angular speed of the bacteria motor is 1447rad/s

t = 4.342 × 10^-3 seconds

Step-by-step explanation:

Hint: Do you remember circular motion in physics???

Okay, let's go

Given:

radius of 1.61 10-8 m

tangential speed at the rim of 2.33 10-5 m/s

Let's recall that angular velocity

ω = Vt/r

Where,

Vt = 2.33 10-5 m/s

r = 1.61 10-8 m

ω = ?

ω = 2.33 ×10-5 m/s = 1447rad/s

1.61 ×10-8 m

Angular speed of the bacteria motor is 1447rad/s

Let's find the elapsed time too

Since The angular velocity is said to be constant, there will be no acceleration (a = 0)

Using:

θ = ωot + (1/2at^2)

t = θ/ωo

(θ = 1 revolution or 2π rad, ωo = 1447rad/s)

t = (2π rad)/(1447 rad/s)

t = 4.342 × 10^-3 seconds