Question 20: A rod of length L0 = 13.0 cm moves along the...

Question 20: A rod of length $L_0 = 13.0$ cm moves along the horizontal direction. The rod makes an angle $\theta_0 = 40.0^\circ$ with the $x'$ axis of its own moving reference frame $S'$. (a) How fast will the rod need to be traveling for an observer at rest to measure and angle of $\theta = 71.0^\circ$ with the axis $x$ of the rest reference frame $S$? (b) What length would an observer at rest measure for the rod if it was traveling at $v = 0.914c$?

Transcript

00:01 Is length contraction in two dimensions where the length contraction is only happening in one of the two directions.

00:08 So i have the gamma term, which is the lorentz modification scaling factor.

00:17 And i have the ordinary equation for length contractions, l prime equals the proper length divided by gamma.

00:26 We have a rod of length l in a frame that's moving at speed v.

00:31 So ordinarily, you have a stationary frame s and a moving frame s prime, and the left -hand side is as observed from the stationary frame, and you're relating what the length would be in the moving frame.

00:57 In this problem, they inverted the situation.

01:01 So they have the observer being in the stationary frame.

01:09 So they're observing the proper length lp, and then some frame moving speed v away in the same direction is what refers to the length l.

01:23 So it's a subtle thing.

01:25 It inverts the whole problem.

01:27 So just be clear, this is, the length would be more.

01:59 Moving frame.

02:06 Okay, so since this is an inverted situation, this means that what you actually have, the stationary frame is lp, the proper line, and then it's l divided by gamma.

02:21 So that's the real situation here.

02:25 So l is degrees theta from the x -axis, and l -p is theta p.

02:38 So since the speed is only in the x direction, nothing on the y direction.

02:48 There's no length contraction at all in the y direction.

02:52 And we have to find the x and y components of the length on the x and y axis...

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