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I want to describe the motion of a ball that rolls without slipping in a plane where acts a force field not in the direction of the motion. To illustrate better, the ball is put on the origin, there is a field h in y direction, and a velocity v0 in the x direction. There is also a friction force parallel to the plane in a way that the balls always rolls without slipping in the plane. How can I calculate y in function of x?

http://imagizer.imageshack.us/v2/280x200q90/673/08e7ea.png [Broken]

I've tried to solve this, but I'm having problems. I know the only torque acting on the particle is Ff.R (Ff = friction force, R is the radius of the ball). So Ff.R = I.γ (I is inertial momment of the ball, γ is the angular acceleration). If I substitute I by 2/5 MR² and γ by a/R I get Ff = 2/5 Ma. But the problem is there, can I do this substitution? Also, is the direction of the friction force opposite to the instantaneous velocity of the particle? Is the ball is rolling in a way that [itex]\vec{ω}[/itex] is always perpendicular to [itex]\vec{v}[/itex]? I don't know how to go on from there.

http://imagizer.imageshack.us/v2/280x200q90/673/08e7ea.png [Broken]

I've tried to solve this, but I'm having problems. I know the only torque acting on the particle is Ff.R (Ff = friction force, R is the radius of the ball). So Ff.R = I.γ (I is inertial momment of the ball, γ is the angular acceleration). If I substitute I by 2/5 MR² and γ by a/R I get Ff = 2/5 Ma. But the problem is there, can I do this substitution? Also, is the direction of the friction force opposite to the instantaneous velocity of the particle? Is the ball is rolling in a way that [itex]\vec{ω}[/itex] is always perpendicular to [itex]\vec{v}[/itex]? I don't know how to go on from there.

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