Rolling Ball on a Horizontal Bar with Angular Velocity ω

[m_34n814]

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!

 

[DaveC426913]

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[m_34n814]

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.

 

[tiny-tim]

hi m_34n814!

(have an omega: ω and try using the X² icon just above the Reply box )

the https://www.physicsforums.com/showthread.php?t=456090&nojs=1#goto_threadtools" is always perpendicular to v_rel, the velocity relative to the moving frame …

so it's tangential, and has no effect on the radial motion …

you can ignore it ​