A table with smooth horizontal surface is fixed in a cabin that rotates with a uniform angular velocity ω in a circular path of radius R (figure 7-E3). A smooth groove AB of length L (<< R) is made on the surface of the table. The groove makes an angle θ with the radius OA of the circle in which the cabin rotates. A small particle is kept at the point A in the groove and is released to move along AB. Find the time taken by the particle to reach the point B.
The component of force along AB is Fccosθ where Fc is centrifugal force.
If the mass of the particle is m then the centrifugal force will be,
Using Newton’s 2nd law,
So it takes 
to reach the point B
1