The Ruby-throated Hummingbird (Archilochus colubris) can flap its wings with an angular speed of 356 rad/s.

Question

What is the period of its flapping motion?

Answer 1

So Lexi M.,

Think about your data and the physical situation. The angular speed being referred to must be the maximum, at the midpoint of the wingbeat down. (Assume up and down periodic motion). So, the speed is like a graph of a sine wave vs. t. For a simple harmonic motion such as this, it doesn't matter that the wings go up, stop, then come down, stop, and return. It is as if they just kept rotating in a circle with that stated angular speed. And how do you convert that to time domain frequency (per second) or period (seconds)?

Ask yourself, how many radians in the complete circle which represents the "wrapping" of the sine wave from Cartesian to radial coordinates (1 sine wave = 1 complete circle). If you got 2.pi.radians = 1 circle= 1 cycle, congratulations. So convert to cycles, using that info.

That should do it

Answer 2

This is what makes a hummingbird amazing, high frequency flaps...

The angular velocity ω = 356 rad/s

By definition, ω = 2π/T

356 rad/s = 2π/T

T = 2π/356 = 2π rad/356 rad/s (rad's cancel out) ==>( 2 x 3.14 ) / 356 ≅ 0.018 s ( Pretty fast )

Completes one flap cycle in roughly 18/1000th of a second.

Best

Bilal S.