Newton's 2nd Law — Free Body Diagrams

Solving force problems using ΣF = ma and free body diagrams

Golden Rule: Draw one FBD per object. Sum all forces in x and y separately. Each unknown needs one equation — count unknowns and equations before solving.

• Step 1: Identify the system and draw FBDs — For each object of interest, draw it alone and add arrows for: weight (mg downward), normal force (perpendicular to surface), friction (opposing motion), tension, applied forces. Draw forces on the object, not from it.
• Step 2: Choose a coordinate system — For flat surfaces: x horizontal, y vertical. For inclined planes: x along the slope (positive up the slope), y perpendicular to the slope. Tilting the axes reduces the number of force components you need to resolve.
• Step 3: Apply ΣFₓ = maₓ and ΣFᵧ = maᵧ — Sum all force components in x: ΣFₓ = maₓ. Sum all force components in y: ΣFᵧ = maᵧ. For the axis perpendicular to motion, acceleration is zero: ΣFᵧ = 0 (use this to find N or T).
• Step 4: Solve the system of equations — If multiple objects are connected, write equations for each and combine. For Atwood-style problems, define a consistent positive direction (e.g., left object goes down = positive). Substitute known values and solve.