Dynamics: Newton's Laws and Forces — AP Physics 1
1. Newton's Three Laws of Motion ★★☆☆☆ ⏱ 4 min
Dynamics is the foundation of Newtonian mechanics, linking forces acting on an object to its change in motion. Unlike kinematics, which describes *how* objects move, dynamics explains *why* motion changes, and makes up 12-18% of the AP Physics 1 multiple-choice section.
- **Newton's 1st Law (Law of Inertia):** An object maintains constant velocity unless acted on by a net external force. Inertia (resistance to motion change) is proportional to mass.
- **Newton's 2nd Law:** Net external force equals the product of mass and acceleration, as a vector equation.
\vec{F}_{net} = m\vec{a}
For 2D problems, split into independent component equations: $\sum F_x = ma_x$ and $\sum F_y = ma_y$. Acceleration always points in the same direction as net force.
- **Newton's 3rd Law:** For every action force from A on B, there is an equal-magnitude, opposite-direction reaction force from B on A. Force pairs act on *different objects*, so they never cancel out for a single system.
2. Free-Body Diagrams and Common Forces ★★☆☆☆ ⏱ 5 min
A free-body diagram (FBD) is a simplified sketch showing only external forces acting on your defined system. Internal forces and motion vectors are never included.
- Define your system clearly (e.g. only the block, not the incline it rests on)
- Draw a dot to represent the system's center of mass
- Add all field forces (only gravity for AP Physics 1 dynamics) then contact forces
- Draw each force as an arrow from the dot, proportional in length to magnitude
- Label each force with standard notation: $F_g$ (gravity), $F_N$ (normal), $F_T$ (tension), $F_f$ (friction)
Four forces make up 90% of AP Physics 1 dynamics problems:
- **Gravity ($F_g$):** Field force pointing down, magnitude $F_g = mg$, $g=9.8 m/s^2$
- **Normal Force ($F_N$):** Contact force perpendicular to a surface; *not always equal to $mg$*
- **Tension ($F_T$):** Contact force along a taut string, constant magnitude for massless strings over frictionless pulleys
- **Friction:** Contact force parallel to a surface, opposing relative motion, with two types: static (non-sliding) $F_s \leq \mu_s F_N$, kinetic (sliding) $F_k = \mu_k F_N$
Exam tip: Examiners automatically deduct points for incorrect free-body diagrams, even if your final calculation is numerically correct. Double-check your force labels before proceeding.
3. Classic Problem Setups: Inclined Planes and Pulleys ★★★☆☆ ⏱ 5 min
Inclined plane problems are simplified by rotating your coordinate system: align the x-axis parallel to the incline, and the y-axis perpendicular to the incline. This splits gravity into two components aligned with your axes.
F_{g,x} = mg\sin\theta \quad (\text{down the incline}) \\ F_{g,y} = mg\cos\theta \quad (\text{perpendicular into the incline})
For no other forces perpendicular to the incline, normal force equals $F_{g,y}$: $F_N = mg\cos\theta$.
For massless, frictionless pulleys, the pulley only changes the direction of tension, not its magnitude. For an Atwood machine (two masses hanging over a single pulley), define a single positive direction for the entire system to avoid sign errors.
4. Translational Equilibrium ★★★☆☆ ⏱ 4 min
An object is in translational equilibrium when the net external force acting on it is zero: $\vec{F}_{net} = 0$. This means acceleration is zero: the object is either stationary (static equilibrium) or moving at constant velocity (dynamic equilibrium). For 2D problems, this gives two independent rules:
\sum F_x = 0 \quad \sum F_y = 0
Common Pitfalls
Why: Students assume equal and opposite forces cancel, but they act on different objects
Why: Students overgeneralize the horizontal flat surface case
Why: Students mix up the two friction types and their formulas
Why: Students confuse forces with their resulting motion
Why: Students forget standard AP Physics 1 problem assumptions