A pendulum's linear and angular momentum change as it swings due to the influence of gravity, which increases its velocity. The magnitude of momentum varies as the pendulum moves along its arc, while the direction of momentum also shifts, remaining tangential to the path. To analyze these changes, one can apply the conservation of mechanical energy to determine the speed at different points in the swing. By calculating the velocity, the corresponding linear momentum can be established, followed by the determination of angular momentum using its definition. Ultimately, both linear and angular momenta are found to change throughout the pendulum's motion.