- #1

- 29

- 9

https://www.physicsforums.com/attachments/266688

Since this is just a geometry problem, after some calculations I reach the following results:

[tex]x=R(\sin(\omega T)-\omega T \cos(\omega T))[/tex]

[tex]y=R(\cos(\omega T)+\omega T \sin(\omega T))-R[/tex]

And it looks fine. I can also differentiate two times with respect to T to get the accelerations:

[tex]a_x=R\omega^2(\sin(\omega T)+\omega T \cos(\omega T))[/tex]

[tex]a_y=R\omega^2(\cos(\omega T)-\omega T \sin(\omega T))[/tex]

Ok, I'm quite convinced those expressions are right.

But now I imagine the problem from the rotating frame point of view. The trajectory of the released object would look more or less like the red dot arrow I think, as shown in the image below:

https://www.physicsforums.com/attachments/266685

Since no real force is acting on the object, in this case I have to explain the movement of the object in terms of two fictitious forces: the centrifugal force, responsible of movement along y direction, and the Coriolis force responsible of the movement along x direction, I think. For a 2D problem, we can write the acceleration as:

[tex]\vec a=\vec a_r+\vec a_\theta= (\ddot r-\dot\theta^2r)\hat r + (r \ddot \theta + 2 \dot \theta \dot r) \hat \theta[/tex]

But here I don't understand how to introduce the angular speed of the rotating frame, so I've not succeeded to formulate the problem in terms of the fictitious forces to reach the previous result. If any of you knows, I would be very thankful if you can show me.