Unit 2: Dynamics

Executive Summary

Dynamics explains motion via forces. Newton's three laws are the framework: inertia, F = ma, and action-reaction pairs.

The laws

First law: an object maintains constant velocity unless a net force acts. Second law: $\vec{F}_{net} = m\vec{a}$ — acceleration is proportional to net force, in its direction. Third law: forces come in pairs on DIFFERENT objects, equal in magnitude and opposite in direction.

Force analysis

Draw a free-body diagram: identify every force (gravity, normal, tension, friction, applied). On an incline, weight splits into $mg\sin\theta$ (along) and $mg\cos\theta$ (perpendicular); the normal force equals $mg\cos\theta$. Friction: static up to $f_s \le \mu_s N$ (object at rest), kinetic $f_k = \mu_k N$ (sliding).

Connected objects

Treat the system as one object to find acceleration ($a = \frac{F_{net}}{m_{total}}$), then isolate one object to find internal forces like tension. Apparent weight in an elevator is the normal force — greater when accelerating up, less when accelerating down.

Exam traps

The action-reaction pair is always on TWO objects — "the table pushes the book" pairs with "the book pushes the table", not with gravity on the book. Normal force is not always mg. Static friction is a "whatever it takes" force up to its maximum. Inertia is not a force.