🔹 1. Kinematics (Motion Basics)
$$v = \frac{dx}{dt}, \quad a = \frac{dv}{dt}$$
When it appears:
- Interpreting motion graphs
- FRQs involving position, velocity, and acceleration
Tip: Always connect equations to graph behavior.
🔹 2. Newton’s Second Law (Core of Mechanics)
$$\sum F = ma$$
When it appears:
- Nearly every FRQ
- Free-body diagram problems
👉 This is the most important equation in the course
🔹 3. Work and Energy
$$W = \int \vec{F} \cdot d\vec{r}$$
$$K = \frac{1}{2}mv^2$$
$$U_g = mgh$$
When it appears:
- Energy conservation problems
- Motion without solving differential equations
🔹 4. Work-Energy Theorem
$$W_{net} = \Delta K$$
When it appears:
- When forces are complicated
- Alternative to Newton’s Laws
🔹 5. Momentum
$$\sum p_{initial} = \sum p_{final}$$
When it appears:
- Collisions (elastic/inelastic)
- Explosions
🔹 6. Impulse
$$J = \int F dt = \Delta p$$
When it appears:
- Force vs. time graphs
- Conceptual FRQs
🔹 7. Circular Motion
$$a_c = \frac{v^2}{r}$$
$$F_c = \frac{mv^2}{r}$$
When it appears:
- Planets, cars, pendulums
- Often combined with Newton’s Laws
🔹 8. Rotation (Torque)
$$\tau = rF \sin \theta$$
$$\sum \tau = I\alpha$$
When it appears:
- Rotational equilibrium
- Rotating systems
🔹 9. Rotational Energy
$$K_{rot} = \frac{1}{2} I \omega^2$$
When it appears:
- Rolling motion
- Energy conservation with rotation
🔹 10. Angular Momentum
$$L = I \omega$$
$$\sum L_{initial} = \sum L_{final}$$
When it appears:
- Rotational collisions
- Systems with no external torque
🔹 11. Simple Harmonic Motion (SHM)
$$a = -\omega^2 x$$
$$T = 2\pi \sqrt{\frac{m}{k}}$$
When it appears:
- Springs and oscillations
- Period calculations
🔹 12. Gravitation
$$F = G \frac{m_1 m_2}{r^2}$$
When it appears:
- Planetary motion
- Satellite problems
🎯 Final Strategy for the Exam
- Focus on:
- Newton’s Laws
- Energy methods
- Momentum conservation
- Always:
- Draw free-body diagrams
- Check units
- Explain reasoning clearly
🚀 Pro Tip
Top scorers don’t just plug into formulas—they:
✔ Choose the most efficient method (force vs energy vs momentum)
✔ Combine multiple concepts
✔ Justify every step
This guide is designed to help you quickly identify which formula to use under exam pressure.