satellites with cameras

A cylindrical satellite has a camera that it can rotate around its centre on a string that can be drawn in or out. If the radius of the satellite is R, the longest length of the string is rl rotating with velocity vl, then at any string length r with velocity v we can draw a relationship. If we regard the mass of the camera as being negligable when compared with the satellite, then angular momentum will be conserved

L = mvr
so, mvr = mvlrl so v = vlrl/r

there is a slot in the centre of the satellite so that the camera can get within the radius of the satellite as the string is drawn in. The tension force on the string is the centripetal force

F = mv^2/ r substituting the previous value for v gives us F = mvl^2rl^2/r3

this cube inverse relationship means the tension force on the string will increase rapidly as the string gets shorter- needs to be strong.

The amount of work to be done to bring the camera into the satellite will be the difference between the kinetic energy at length rl and that at length R

i.e. Change in E = 1/2 mv62 - 1/2 mvl^2

when I substitute in this I get change in E = mvl^2(rl^2-R^2)/R^2

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