I'm no saying you're wrong, but I don't understand it.
What I see is that when you convert from Lucy's time to Betsy's time it converts to 6.8 seconds. Betsy thinks Lucy's clock is slow relative to hers, even slower than Bob's clock is relative to Lucy's clock. There's no gap, just a...
I don't think that works.
Try this -- somebody is traveling at a speed so large that one of his seconds is equal to 1000 of yours. He arrives at your location and you are interested in something that happened 4 second ago by his clock. Then you wait another 4 seconds by your clock.
What kind...
No, I don't think that's right. Both of them see Bob's clock ticking slower. Each of them sees Bob's clock ticking 3.2 seconds while their own ticks 4 seconds.
This is required by SR.
But we can't just add 4+4 to get 8, and we can't just add 3.2 + 3.2 to get 6.4.
Arithmetic doesn't work that...
The way I read it, Betsy's clock will have advanced 4 minutes since she left Lucy. She might not feel it appropriate to count Lucy's 4 minutes, but might instead translate them to the time that seems right for her own frame. But it's a picky point.
I don't see what to do about that. The events...
Yes, but you can't just add velocities. When they're in the same or opposite directions, you add them like this:
V1 + V2 = (V1 + V2)/(1+V1V2) Where V1 and V2 are fractions of lightspeed. Like .6 c.
Ah! I have an alternative view. Betsy need not take Lucy's view of things. From Betsy's point of view, Bob is traveling toward her at .6 c. Lucy is traveling toward her at .88 c.
So from her point of view, Lucy's time is dilated even more than Bob's. If I read it right, not just .8, but .47...
Let's say that 4 minutes has passed on Lucy's clock when she sync's Betsy's clock.
Lucy's situation is exactly equivalent to Bob's, and she has exactly as much reason to think that Bob's time is dilated compared to hers, as Bob has to think her time is dilated compared to his. Her clock reads 4...
I find the discussion about acceleration confusing. I want to avoid that.
So try this scenario: Lucy is traveling at .6c relative to Bob. Just when they reach their point of closest approach, one kilometer, they synchronize clocks.
As their distance increases, each of them sees a red shift...
Curiouschris, it is because the gyroscope is spinning.
Why does that change anything? He's holding the end of a long lever. If he tries to torque up or down, the gyroscope will move sideways. If he tries to torque sideways, the gyroscope will tilt up or down.
He tries to spin it around his...
a sideways force that is getting transformed into an upward force
"... violates conservation of momentum"
Oops. What's the right way to say that?
It creates a torque that tends to rotate the gyroscope at right angles to the direction of motion, that is, up. You don't notice the opposing...
It looks to me like the video A.T. provided explains it, in line with some of DaveC's comments.
When you tilt the rotor sideways, it precesses. One direction it precesses up, the other direction down.
If you turn it in the direction that it precesses up, it is easier to raise it -- you don't...
The Twin Paradox is an application of the simple math of lorentz transforms, and unfortunately it was designed to mystify.
The lorentz transform says that when you assign velocity to another observer, his distances contract and his clock slows. At the same time, when he assigns the velocity to...
Reviewing this problem, I got
83.3*10^-9 * .95 * 3.0*10^8 = 23.74 meters
A more precise answer for the time is lower, a more precise number for lightspeed is lower. But the book's answer was 24.0, about 1% higher than my answer and their answer is claimed good to one part in 240 or so.
I...