$(\frac{d\vec{p}}{dt})\parallel = \vec{F}_{net}\parallel$ is the rate of change of the amgnitude of the momentum.
$(\frac{d\vec{p}}{dt})\perp = \vec{F}_{net}\perp$ is the rate of change of the direction of the momentum, which is numerically equal to the sideways (perpendicular) component of net force. Other associations:$$|(\frac{d\vec{p}}{dt})\perp| = |\vec{p}|\frac{|\vec{p}|}{R}$$$$|(\frac{d\vec{p}}{dt})\perp| = |\vec{p}||\frac{d\hat{p}}{dt}| = |\vec{p}|\frac{|\vec{p}|}{R} = \frac{\gamma mv^2}{R}$$$$|\vec{a}\perp| = |(\frac{d\vec{v}}{dt})\perp| = |\vec{v}||\frac{d\hat{v}}{dt}| = |\vec{v}|\frac{|\vec{v}|}{R} = \frac{v^2}{R}$$$$\frac{d\vec{p}}{dt}\leftarrow\vec{F}_{net}$$
