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 1.70e-8 m, and a tangential speed at the rim of 2.32 e-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?
r = 1.70*e^-8 = 5.70*10^-4 m.
C=pi*D=3.14*(2*5.70*10^-4)=3.58*!0^-3 m
a. V = 2.32*e^-5 = 0.01563 m/s.
Va = 0.01563m/s * 6.28Rad/0.00358m = 27.4 Rad/s = Angular velocity.
b. d = Va*t.
t = d/Va = 6.28Rad / 27.4Rad/s=0.229 s.
To solve these problems, we need to use the relationship between angular velocity (ω), tangential speed (v), and radius (r).
(a) The angular speed can be calculated by dividing the tangential speed by the radius. So we have:
angular speed (ω) = tangential speed (v) / radius (r)
ϖ = v / r
Substituting the given values:
angular speed (ω) = 2.32e-5 m/s / 1.70e-8 m = 1.364e3 rad/s
Therefore, the angular speed of the bacterial motor is 1.364e3 rad/s.
(b) To find the time it takes for the motor to make one revolution, we need to consider the relationship between angular velocity and time.
Since 1 revolution is equal to 2π radians, we can use the formula:
Time (t) = (2π) / ω
Substituting the calculated angular speed from part (a):
Time (t) = (2π) / (1.364e3 rad/s)
Calculating this expression, we get:
Time (t) = 1.459e-3 s
Therefore, it takes the bacterial motor approximately 1.459 milliseconds to make one revolution.