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 1.1x10-8m, and a tangential speed at the rim of 2.0x10-5 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?
I was able to answer a) but I am not sure what equation to use for part b. Below is what I have calculate. A helpful nudge in the right way would be great!
VT = 2.0x10-5 m/s
r = 1.1x10-8m
w = 1818.18 rad/s
a)w = (2.0x10-5 m/s = 1.1x10-8m)t
a) angular speed = w = V/R
= 2*10^-5/1.1*10^-8 = 1818 rad/s
b) Period = (2 pi)/w = 3.36*10^-3 s
Thank you!
You answer is correct. My calculator is giving me 0.00345. I am not sure why. Do you think that it could be a setting that I need to change?
Never mind - I figured it out.
Thanks for your help!
my calculator is giving me 0.00345. How did you figure it out?
To answer part (b) of the question, we can use the relationship between angular speed (ω) and time (t) to calculate how long it takes for the motor to make one revolution.
The angular speed (ω) is given by:
ω = v/r
Where:
ω = angular speed (in radians per second)
v = tangential speed at the rim of the motor (in meters per second)
r = radius of the motor (in meters)
From part (a), we know that the angular speed is 1818.18 rad/s.
To calculate the time (t) for one revolution, we need to determine how much time it takes for the motor to complete one full revolution, which is equivalent to completing a full circle (2π radians).
The equation relating angular speed (ω) to time (t) for one full revolution is:
ω = 2π/t
Rearranging the equation to solve for time (t):
t = 2π/ω
Substituting in the given value for angular speed (ω):
t = 2π/1818.18 rad/s
Calculating this expression will give you the answer for part (b), which is the time it takes for the motor to make one revolution.
I hope this helps! Let me know if you have any further questions.