Newton’s Laws in Three Dimensions

It is now fairly straightforward to extend Newton's laws to three dimensions:

Newton's first law

If all three components of the total force on an object are zero, then it will continue in the same state of motion.

Newton's second law

The components of an object's acceleration are predicted by the equations ax = Fx,total/m , ay = Fy,total/m , az = Fz,total/m .

Newton's third law

If two objects A and B interact via forces, then the components of their forces on each other are equal and opposite: FA on B,x = -FB on A,x , FA on B,y = -FB on A,y , FA on B,z = -FB on A,z .

Forces in perpendicular directions on the same object.

Discussion Questions

A	The figure shows two trajectories, made by splicing together lines and circular arcs, which are unphysical for an object that is only being acted on by gravity. Prove that they are impossible based on Newton's laws.