- #1
meson0731
- 14
- 0
Homework Statement
Find the curvature of the spiral of Archimedes r = 2θ
Homework Equations
||v x a || / ||v||^3
The Attempt at a Solution
I tried to convert the polar equation into parametric and got
x = 2θsinθ
y = 2θsinθ
z = 0
I think took the derivative of x y and z and got
x' = -2θsinθ + 2cosθ
y' = 2θcosθ + 2sinθ
z' = 0
I then put them into vectors and used the cross product to get v x a and got the magnitude to be 4θ^2. I found ||v||^3 to be 8θ^3 so I got || v x a || / ||v^3|| = (1/2θ) .