Spinning wheel question

Question

If a wheel is being recorded in 24 frames per second and has 6 evenly spaced spokes with 13 inches in radius. What is the slowest possible speed it mi/hr that the wheels appear to spin backwards.

I tried to use the equation v = rw but am having trouble understanding what the frequency will be to make the wheels appear to spin backwards

the question just indicates frames per second of the video camera — user12834342423324, Feb 14 '14 at 06:04
First, work out the slowest speed at which the wheel appears stationary. — Gerry Myerson, Feb 14 '14 at 06:05

score 1 · Answer 1 · answered Feb 14 '14 at 06:06

The wheel seems to stand still if the speed is so that with every frame it rotates to the next spoke, i.e. at 6 frames per round or 4 rounds per second. (The same occurs at 8,12, 16, ... rounds per second). At half that speed, the spokes seem to flicker and this is the speed singularity where the wheel switches from apparent forward to apparent backward rotation. Finally convert ritaion to velocity (yes, $v=\omega r$ is what is needed there)

so would f = 1/4 then w = 2pi*f – user12834342423324 Feb 14 '14 at 06:09 — user12834342423324, Feb 14 '14 at 06:09

Spinning wheel question

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