On television, rotating objects such as wagon wheels and airplane propellers oft

Question

On television, rotating objects such as wagon wheels and airplane
propellers often appear to be moving very slowly or even backwards. This is
a result of aliasing, caused by the sampling rate of the video (30 frames
per second) being less than twice the frequency of the rotational motion. To
understand this, imagine we paint one of the blades of an airplane propeller
so that we can identify it from the other blades. We will then turn the
propeller at 33 rotations per second, in a clockwise direction. In frame
number 1 of our video sequence, the marked blade happens to be exactly at
the top of the propeller.

a. How many rotations does the marked blade make between two successive
frames?
b. Draw a sketch of how the propeller would appear in frames 1, 2, 3 and 4.
c. How many frames does it take for the marked blade to again appear at the
top?
d. What rotational frequency is (c) in rotations per second?
e. Is this apparent rotation clockwise or counterclockwise?
f. Explain using Fig. 3-4 how the marked blade's actual frequency, the frame
rate, and the marked blade's observed frequency are related.
g. Repeat (a) to (f) when the propeller is turning at 57 rotations per
second.

Explanation / Answer

a. the blade will complete 33/30 rotations per frame.
b. the sketch will resemble a wagon wheel with 10 pegs, but only the first 4 of them, (the way i like to approach this is that you cancel out the full integers when doing the division on part a. so that means 33/30=1.1 cancel out the full integer which is the 1 and you are left with 0.1 or 1/10) because the frame will catch the blade 3/30 or 1/10 rotations from the previous caught frame.

c. 10 frames because the blade moves 1/10 of a rotation per frame

d. c= 3 rotations per second (1/10*30=3)

e. the apparent rotation is clockwise

f. dont have the figure 3-4..

g. changing the letters to numbers for the repeat

1. blade completes 57/30 rotations

2. the sketch will be the same as the first, however the sketch will go counterclockwise

3. 10 frames the apparent speed is going to be the same as the first but it is going in the opposite direction

4 c=3 rotations per second

5. the apparent rotation is counterclockwise

hope this helps

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