High speed cameras are used to photograph events which take place too quickly to

Question

High speed cameras are used to photograph events which take place too quickly to be seen by the human eye. One such high speed camera is composed of a rotating film drum, a rotating shutter and some miscellaneous optics. The film is fastened along the outside of the drum (along its entire circumference) and the drum is driven by high pressure gas.

You desire to photograph the dynamics of a bumblebee in flight and estimate that its wings flap somewhere about 10,000 times a second. The radius of the film drum isr = 0.501 mand you've loaded it with35mmfilm.

Number=

? =

? =

What was the angular acceleration of the film drum after turning off the gas?

? =

Explanation / Answer

1)

2r/35e-3 = 2*3.1416*0.501/35e-3 = 89.940 89.9

2)

w = 2 * 3.1416 * 20000 = 125664 rad/s

3)

20000/89.940 = 222.37

2 * 3.1416 * 222.37 = 1397 rad/s

4)

= 1397.195/(2*60) = 11.6 rad/s2

5)

= 0.5 t^2 + t

= -0.5 * 11.643 * (2*60)*(2*60) + 1397.195 * (2*60)

= 83833.8 rad

83833.8/2/3.1416 = 13343 rev

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