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 1.9x10-8m, and a tangential speed at the rim of 2.5x10-5 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?
v=ω•R, => ω=v/R,
T=2π/ω
To find the angular speed and the time taken for one revolution, we can use the formula:
angular speed = tangential speed / radius
(a) Angular speed:
Angular speed = 2.5x10^(-5) m/s / 1.9x10^(-8) m
Angular speed ≈ 1.32x10^3 rad/s
The angular speed of the bacterial motor is approximately 1.32x10^3 rad/s.
(b) Time taken for one revolution:
To find the time taken for one revolution, we need to determine the angle covered during one revolution. A full revolution covers 2π radians.
Time taken = 2π / angular speed
Time taken = 2π / (1.32x10^3 rad/s)
Time taken ≈ 4.78x10^(-3) s
The motor takes approximately 4.78x10^(-3) seconds to make one revolution.