# Hw 14 Problem 5

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A deep-space vehicle moves away from the Earth with a speed of 0.870c. An astronaut on the vehicle measures a time interval of 2.45 s to rotate her body through 1.00 rev as she floats in the vehicle. What time interval is required for this rotation according to an observer on the Earth?

Since the question asks, What time interval is required for this rotation according to an observer on the Earth? I figure we're looking for t'?

So t'=x'/u'  I tried to calculate x' by x/gamma..since x is given in units of rev. I ended up getting t' in units of revolutions/c but the question wants the units to be seconds.

If you could guide me where I'm going wrong, would be helpful

For this question, the astronaut's rotational motion is an event and needs not to be calculated for its rotational speed in the new frame. For this event, it takes 2.45 s in the space ship, which is the proper time the astronauts on the space ship would observe. The question is then to find out what the earth based observer would measure the time duration for this rotation. So just use the time dilation relation, we can find the answer: $$\Delta t=\gamma \Delta t_p$$