t has been chosen so that r'.r'=1
show that r'.r''=0
The Attempt at a Solution
Clearly what is being described is circular motion about a unit circle. And using the equation for a unit circle its easy to show that r'.r''=0 Velocity is tangent to the circle, acceleration is inward and therefore the dot product of the two is zero.
What I am having trouble with is showing for the general solution.
r'.r'=|r'||r'|cos(theta) = 1
theta is zero, and therefore |r'| is 1 , this isn't particularly helpful.
r''.r'=|r''|cos(theta) (theta not zero)
Expanding in parametric form doesn't seem to help either.
I am at a loss.