Suppose an object moves on the surface of a sphere with magnitude of r(t) constant for all t. Show that r(t) and a(t) = r''(t) satisfy r(t) : a(t) = -(mag(v))^2
( :=dot product)
Thanks! :)
Hey jessicadowning.
For this problem consider that in polar co-ordinates, you are moving at the same speed on the sphere which means dr/dx where x is a direction vector in terms of your angles (you will have two for a sphere) will be constant. So you have a total differential (in terms of the rate of change with respect to the angles) that is the same everywhere.