A positive caster angle in shopping carts causes the wheels to self-align due to the pivot axis being positioned behind the wheel axis, which creates a force that pushes the wheels back to a straight position when the cart is in motion. Conversely, a negative caster angle results in instability, as the wheels are less likely to return to a straight line, leading to difficulty in steering. The discussion emphasizes the importance of caster angle in both shopping carts and race cars for maintaining directional control. Participants seek a visual force diagram to better understand these dynamics. Understanding caster angles is crucial for optimizing wheel paths in various vehicle designs.