A point on the edge of a satellite with mass m moves with...

A point on the edge of a satellite with mass $m$ moves with speed $v_0$ at a distance of $r$ from the central axis of rotation. The satellite unfolds its panels, increasing its radius to $2r$ but the mass remains the same. What is the final speed $v$ of a point at the edge of the satellite's panels and how does it compare to its initial speed?

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Transcript

00:05 So we're asked to figure out the speed of a satellite in circular orbit around the earth.

00:19 Well, i know that the square of the period is 4 pi r cubed, 4 pi squared r cubed over gm.

00:36 But the period is, well, let's not go to that yet.

00:51 Just take the square root of both sides, r cubed over g .m.

01:04 Now, the period is 2 pi r over the speed.

01:12 Or rather, the speed of the satellite is 2 .5.

01:21 R over the period, which is 2 pi square root of r cubed over gm.

01:35 The 2 pi cancels out.

01:41 This and this cancel out.

01:44 Two of the rs in the denominator cancel out.

01:48 And so it is the square root of gm over r, which i probably could have just written down without going through this.

02:00 But anyway, square root of gm over r.

02:14 Okay, let's move on to b.

02:25 So the satellite breaks into two masses, m and 4m.

02:47 And it tells us that the smaller piece is stationary with respect to earth and falls directly toward, which has to figure out the speed of the larger piece.

03:15 So i'm going to write that the kinetic energy before the explosion equals the kinetic energy after the explosion of the smaller one, plus the kinetic energy after this explosion of the larger one.

03:43 So the kinetic energy at the beginning is one -half times m, although the mass at the beginning is 5m...

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