# Nonuniform circular motion

A ball rocks around an arc. In the following illustration, the ball reaches the end of the arc (its velocity magnitude is zero at that particular moment).

Now, I want to know which forces are acting on that ball at that particular moment. We have the tension force $$\vec T_2$$ acting on the ball, which is the centripetal force. We also have the gravity which consists of two Cartesian components: radial $$mg \cos\alpha$$ and tangent $$mg \sin \alpha$$. In the radial axis our net force $$\vec T_2 - mg \cos \alpha = mv^2 / R$$ is zero because $$v = 0$$. However, in the tangent axis our net force is not zero - $$mg \sin \alpha$$. My question is - how it could be if the ball at that particular moment is not moving because he reaches the edge of his trajectory? If it doesn't move then there should be some opposite force acting on it. My intuition says that that tangent force $$mg \sin \alpha$$ is forcing the body to slow down in that direction, so it slowly "cancels" the force which caused the body to move initially. But how can I describe it with formulas and/or illustrate it from the point of view of inertial system (i.e., Earth)?

• The instantaneous velocity tells you nothing about the force. $F=ma$. – DilithiumMatrix Mar 13 '13 at 15:00