please give me FULL ANSWER WTIH COMPLETE EXPLANATION Consider the wheel below wi

Question

please give me FULL ANSWER WTIH COMPLETE EXPLANATION

Consider the wheel below with six identical spokes. It is rotating clockwise at 2 revolutions per second. The period of a signal is the smallest unit of time T for which a signal repeats itself. Given the above definition, what is the frequency omega0 of the rotating wheel signal. Hint: it is not 4 pi rad /s. If I take a picture of this wheel 20 times a second and play this back as an animation, in which direction and at what speed will the wheel appear to be rotating? Hint: it may help to model the signal as sin(omega0t).

Explanation / Answer

since it has 6 identical spokes so the rotating wheel signal has frequency of 2*6=12 Hz

so w(omega)=24*(pi)

we take 20 pictures per second.so in any 2 consecutive pictures angle rotated by any referance spoke is 2*2*(pi)/20=pi/5 radians = 36 degrees.

difference between any 2 spokes = 60 degrees.

so from referance position,1 spoke is 36 degrees ahead and other is 24 degrees behind.(seeing in clockwise sense)

hence on keeping these 2 consecutivly,rather gives a feeling of wheel moving in anti-clockwise direction with frequence 'f' rather than clockwise direction. where :

f=(24 degree) * 20/(360 degree)=4/3 Hz.

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