How do you prove...?

Question

If an object is moving on the surface of a sphere, its postion and velocity vectors must be perpendicular.

Answer 1

Since it's instantaneous velocity is tangent to the surface and the position vector (from the center of the sphere) is normal to the surface, they're perpendicular pretty much by definition.


Doug

Answer 2

well, you can prove it by proving that it is not any other direction.


in the limit that you look at an instantanious velocity if the direction is anything other than tangent to the sphere the possition of the object will no longer be on the surface of the sphere.

and we all know that the tangent is described by being normal to a vector from the orgin to the surface.