# Homework Help: Changing from cartesian to polar

1. Sep 15, 2008

### CompStang

1. The problem statement, all variables and given/known data
A particle moves in a two-dimensional orbit defined by:
x(t)= A(2$$\alpha$$t-sin($$\alpha$$t)
y(t)= A(1-cos($$\alpha$$t)
a) Find the tangential acceleration a_t and normal acceleration a_n as a function of time where the tangential and normal components are taken with respect to the velocity.

2. Relevant equations
x''(t)= A$$\alpha$$^2sin($$\alpha$$t)
y''(t)= A$$\alpha$$^2cos($$\alpha$$t)

3. The attempt at a solution
I found both the velocity and acceleration for both x and y vectors given and realize that a(t)= x''(t)i$$\widehat{}$$+ y''(t)j$$\widehat{}$$
also I know that:
a(t)=a_nr$$\widehat{}$$+a_t$$\phi$$$$\widehat{}$$
So I need to find x" and y" in terms of polar to get the answe for a_n and a_t

2. Sep 15, 2008

### CompStang

sorry all these alphas are not supposed to be raised to the power of there previous components. it is supposed to be for example x(t)=A(2*(alpha)*t-sin((alpha)*t).....and so on