Rolling ball, change of direction

[jonbarril]

Say I have a magic way to exert lateral forces on a free-rolling ball on a plane, with no slipping. Say I apply a force for a given period from the South, the ball starts rolling to the North and attains a constant speed. Then I suddenly apply the same force for the same period but from the West. What is the resulting path of the ball on the plane? What is the path of the balls apparent axis of rotation (how does it change from East-West to eventually North-South, does it remain horizontal)?

Thanks
--jon

 

[A.T.]

If you apply just a force at the ball's CoM, and it starts rolling, the you must have friction. If you then apply the lateral force you will have an interaction of friction gyroscopic effects, which can get quite complex and counter intuitive:

 

[Lnewqban]

Forces are associated to accelerations.
How do you believe the trajectory will change?

 

[jonbarril]

It has been a long while since I took physics. I think the gyroscopic effect will work in favor of helping to turn the ball to the East. My guess is that the ball would end up rolling North-East. Not sure if the axis of rotation would stay flat. This is all complete conjecture. I'm hoping folks out there can give a more informed description of the ball's motion.