B A doubt about tangential and normal aceleration, pilot g forces

[farolero]

What is the y component of the velocity of the astronaut? (answer in terms of v and αα\alpha).
What is the y component of the velocity of the spot? (answer in terms of R and ωω\omega).
Is the y component of the velocity of the astronaut the same as the y component of the velocity of the spot? (yes or no).

vsinalpha.
wR.
yes.Edit:

Also I was wondering if your frame reference is rotating with the tube or not? I didnt understand that part.

 

[jbriggs444]

vsinalpha
wR
yes

Good. Now that means that one can write:
$$v \sin \alpha = vy_{astronaut} = vy_{spot} = \omega R$$
Solving for v...
$$v = \frac{\omega R}{\sin \alpha}$$

 

[farolero]

Yes but is it the frame reference rotating with the tube? because otherwise I am not sure the aswer to the last question is yes.

From a fixed reference the Vy of the astronaut would be Vsin alpha plus the speed of the tube at that point.

 

[jbriggs444]

Yes but is it the frame reference rotating with the tube? because otherwise I am not sure the aswer to the last question is yes.

*heavy sigh*
There is a reason that I said "stationary" when I asked you to imagine the cartesian coordinate grid.

From a fixed reference the Vy of the astronaut would be Vsin alpha plus the speed of the tube at that point.

That is not correct and does not match the answer you gave previously. You have already agreed that the Vy of the astronaut is equal to the Vy of the tube.

Unless the walls of the tube have holes in them, the two velocities must match.

 

[farolero]

Ok i see you took an stationary reference i was not sure if it was stationary with the tube.

What you said seems only valid for that special position, if the tube is offset 45º from the x reference the Vy of the point is wrsen45 but the vY of the astronaut would actually be the net tangential velocity of the astronaut so Vy= Vt( supposing the trajetory of the astronaut is offset 45º from radially). And in this case the Vy of the point wouldn't be equal to the Vy of the astronaut.

So your main assumption to solve the problem though antiintuitive is not right.

Your assumption that the Vy of the point= Vy of the astronaut is only valid if you take a rotating reference with the tube, as a matter of fact you did so putting the x axe along the tube

 

[jbriggs444]

Ok i see you took an stationary reference i was not sure if it was stationary with the tube.

What you said seems only valid for that special position, if the tube is offset 45º from the x reference the Vy of the point is wrsen45 but the vY of the astronaut would actually be the net tangential velocity of the astronaut so Vy= Vt( supposing the trajetory of the astronaut is offset 45º from radially). And in this case the Vy of the point wouldn't be equal to the Vy of the astronaut.

That is not correct. If the tube is offset by 45 degrees, then you just unstick the coordinate grid from the wall, rotate it by 45 degrees and stick it back down again.

Or you can do the analytical geometry to demonstrate that it works even if you do not unstick the grid.

Your basic problem is your unwavering conviction that you are right. Please review Mark Twain's admonition. You are so far wrong that it is not even entertaining.

 

[farolero]

That is not correct. If the tube is offset by 45 degrees, then you just unstick the coordinate grid from the wall, rotate it by 45 degrees and stick it back down again.

Then if you unstick and stick the x axe along the tube youre taking a rotational frame with the tube.

Ill demonstrate how the Vy of the point is not the Vy of the astronaut analitically:

When the tube has an angle of 45º with the x reference you stop it with an exterior torque, so the w is zero, then Vy of the spot=0 but Vy of the astronaut doesn't equal zero, so Vy of the astronaut is not equal to Vy of the spot bringing down your original assumption

I think mark twain quote is more appropiate for the teacher than for the student.

 

[Doc Al]

I think it's high time to close this thread.

@farolero: Please review the entire thread, paying close attention to jbriggs444's very patient explanations.