Rolling Ball on a Horizontal Bar with Angular Velocity ω

AI Thread Summary
A bar of length L is rotating with angular velocity ω, and a ball of mass m rolls on it without friction, starting with an initial velocity u0. The discussion focuses on the forces acting on the ball, specifically the Coriolis and centrifugal forces, and how to relate the ball's velocity (v) to its position (x) to solve the motion equations. The key equation derived is d²x/dt² = 2ωv, which needs to be connected to find the time when the ball reaches the end of the bar at x = L. Participants emphasize understanding the direction of forces and the ball's movement in a non-inertial reference frame. The conversation highlights the importance of correctly applying physics principles to solve the problem.
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bar (length L) is turned with angular velocity ω, on a horizontal level. Αt length of the bar, there is a ball (mass m) which rolls (We suppose that there is no friction force). The ball begins from constant utmost the bar with initial velocity u0. When the ball reaches in the L?

Can you help me!?
Thank you!
 
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First of all, according to the no Inertial Reference Frame there will be 2 Forces (the once is Coriolis and the other once is Centrifugal).
We can write:
xdx^2/dt^2=-2w*v=-2w*v(z*y)=2w*v*x
or d^2x/dt^2=2*w*v
where v is the velocity of the ball.
I think that I have to write v connection x, and then I can solve this differential equation…
Then I will solve the equation x=L to find t.

My problem is how can I connect v and x.

I think that my problem is the direction of these 2 Forces
In fact, I think that I haven’t understand how the ball will move.
 
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