Question

The flagella of a bacterium can rotate very rapidly. If a flagellum rotates at a uniform angular speed of 1000 rad/sec, how long does it take for the flagellum to complete one–half of a rotation?

a) 0.001 seconds
b) 0.0005 seconds
c) 0.00025 seconds
d) 0.002 seconds

Answer 1

To calculate the time it takes for a bacterium's flagellum rotating at 1000 rad/sec to complete half a rotation, we divide π radians by the angular speed, resulting in approximately 0.003 seconds. The closest answer option is d) 0.002 seconds.

Step-by-step explanation:

The flagellum of a bacterium rotating at a uniform angular speed of 1000 rad/sec needs to complete half of a rotation, which is equivalent to π radians (since 2π radians is one full rotation). To find the time it takes for half a rotation at this speed, we can use the formula τ = θ / ω, where θ is the angular distance (in radians) and ω is the angular speed (in radians per second).

Time for half rotation = θ / ω = π radians / 1000 rad/sec = 0.00314 seconds ≈ 0.003 seconds.

Therefore, the time it takes for the flagellum to complete half a rotation is about 0.003 seconds, which is not exactly one of the provided options, but the closest answer is option d) 0.002 seconds.