Forces and Newton's Laws

The Three Laws

Newton's first law: constant velocity (including rest) means zero net force. The second law quantifies dynamics: $F_{net} = ma$ The third law pairs equal and opposite forces acting on different bodies — they never cancel within one free-body diagram.

The Common Forces

Weight is $mg$ downward. The normal force is perpendicular to the surface and adjusts to circumstances — it is not automatically $mg$. Friction opposes relative sliding: $f_s \le \mu_s N, \qquad f_k = \mu_k N$ Static friction takes whatever value is needed up to its maximum and exceeds kinetic friction. Tension is uniform in an ideal rope. For circular motion, some real force (tension, gravity, friction, normal) supplies the centripetal requirement $F_c = mv^2/r$.

Inclined Planes

Decompose gravity along and perpendicular to the incline: the component pulling down-slope is $mg\sin\theta$ and the perpendicular component is $mg\cos\theta$, so $N = mg\cos\theta$ on a frictionless analysis. Draw the free-body diagram, pick axes along the incline, and apply $F_{net} = ma$ per axis.

Key Takeaways

• Zero net force means constant velocity, not necessarily rest.
• Normal force is situational — elevators and inclines change it.
• $mg\sin\theta$ drives sliding; $mg\cos\theta$ sets the normal force.
• Centripetal force is a role played by real forces, never a separate force.