Show that the acceleration vector in polar coordinates is given by: a= dt
dv
​
=[ dt 2
d 2
r
​
−r( dt
dθ
​
) 2
] r
^
+(r dt 2
d 2
θ
​
+2 dt
dr
​
dt
dθ
​
) θ
^
102 Classical Mechanics: A Computational Approach One possible method is by taking the time derivative of the velocity vector v= dt
dr
​
= dt
dr
​
r
^
+r dt
dθ
​
θ
^
and then using the derivatives of the unit vector's dt
d
​
θ
^
and dt
d
​
r
^
derived in this chapter.