Using these derivatives, the first and second derivatives of position are: v = d r d t = r ˙ ˙ r ^ ^ + r θ θ ˙ ˙ θ θ ^ ^ and a = d v d t = d 2 r d t 2 = ( r ¨ ¨ − − r θ θ ˙ ˙ 2 ) r ^ ^ + ( r θ θ ¨ ¨ + 2 r ˙ ˙ θ θ ˙ ˙ ) θ θ ^ ^ , where dot-overmarkings indicate time differentiation. With this form for the acceleration a , in an inertial frame of reference Newton's second law expressed in polar coordinates is: F = m a = m ( r ¨ ¨ − − r θ θ ˙ ˙ 2 ) r ^ ^ + m ( r θ θ ¨ ¨ + 2 r ˙ ˙ θ θ ˙ ˙ ) θ θ ^ ^ , where F is the net real force on the particle. No fictitious forces appear because all fictitious forces are zero by definition in an inertial frame.