Physics Tutor

Diagram Patterns

Free Body Diagram (ASCII)

                 N (Normal)
                 ↑
                 │
    f ←─────────┼─────────→ F (Applied)
    (friction)  │      
                │
                ↓
                W (Weight = mg)

Vector Addition

flowchart LR
    A[Vector A] --> C[Resultant R]
    B[Vector B] --> C

Circuit Diagram (ASCII)

    ┌────/\/\/\/────┐
    │      R        │
  ──┴──           ──┴──
  + │ -  Battery   │
  ──┬──           ──┬──
    │               │
    └───────────────┘

Problem-Solving Framework

General Steps

1. Draw a diagram - Visualize the situation
2. List knowns and unknowns - Organize given data
3. Choose equations - Match variables to formulas
4. Solve algebraically first - Keep symbols until the end
5. Substitute values - Include units
6. Check answer - Units, magnitude, direction

Kinematics Problem Pattern

Given: v₀, a, t (or any 3 of 5 variables)
Find: x, v (or remaining variables)

Equations to choose from:
1. v = v₀ + at
2. x = v₀t + ½at²
3. v² = v₀² + 2ax
4. x = ½(v₀ + v)t

Force Problem Pattern

1. Draw free body diagram
2. Choose coordinate system
3. Apply ΣF = ma in each direction
4. Solve system of equations

Key Concepts Summary

Newton's Laws

Energy Conservation

$$E_{total} = KE + PE = \text{constant (in isolated system)}$$

$$KE = \frac{1}{2}mv^2 \quad PE_{gravity} = mgh \quad PE_{spring} = \frac{1}{2}kx^2$$

Momentum Conservation

$$p = mv \quad \Sigma p_{before} = \Sigma p_{after}$$

Common Mistakes to Avoid

1. Forgetting to convert units (km to m, hours to seconds)
2. Wrong sign convention (acceleration vs. deceleration)
3. Using wrong kinematic equation (check which variable is missing)
4. Ignoring friction when it's present
5. Confusing instantaneous vs. average values