v_theta = r*(dtheta/dt)

If you take the time derivative of this, you get the acceleration in the theta direction

a_theta = (dr/dt)*(dtheta/dt)+r*(d^2 theta / dt^2)

This is wrong. Can anyone tell me why? The accepted answer is

a_theta =

**2***(dr/dt)*(dtheta/dt)+r*(d^2 theta / dt^2)

Where does that factor of 2 come from?

Edit: The 2 pops up because the unit vectors in cylindrical coordinates are time-dependent too. Oops! Been too long since I've taken vector calc I guess