First law (Inertia): An object continues in its state of rest or uniform motion unless acted upon by a net external force. Inertia is proportional to mass.
Second law: F = ma (F_net = rate of change of momentum = dp/dt). Unit: Newton = kg·m/s².
Third law: For every action, there is an equal and opposite reaction. Forces in action-reaction pairs act on DIFFERENT bodies.
Free Body Diagram (FBD): Draw all forces on the body of interest. Normal force (N) perpendicular to surface. Weight (mg) downward. Tension (T) along string. Friction (f) opposing motion.
Static friction: f_s ≤ μ_s N. Adjusts to oppose tendency of motion. Maximum static friction = μ_s N (limiting friction).
Kinetic friction: f_k = μ_k N. Constant once sliding. μ_k < μ_s (easier to keep moving than to start).
Inclined plane: Body on incline angle θ. N = mg cos θ. Net force down incline = mg sin θ - f = mg sin θ - μ_k mg cos θ = mg(sin θ - μ_k cos θ). Angle of repose: tan θ = μ_s (body just begins to slide).
Connected bodies: Block A (m₁) and B (m₂) on surface connected by string. Pulling force F on B. Tension T = m₁F/(m₁+m₂). Acceleration a = F/(m₁+m₂).
Work: W = F·d·cos θ. Positive work: F has component in direction of displacement. Zero work: perpendicular force (centripetal force). Negative work: F opposes displacement (friction, braking).
Kinetic energy: KE = ½mv². Work-energy theorem: W_net = ΔKE = ½mv² - ½mu².
Potential energy: Gravitational PE = mgh. Spring PE = ½kx². Conservative forces: work done independent of path; work done in closed path = 0.
Conservation of energy: KE + PE = constant (no non-conservative forces). Power P = W/t = Fv.
Elastic collision: Both KE and momentum conserved. For equal masses: velocities exchange. For m₁ >> m₂: heavy body barely slows, light body moves at 2× heavy body's speed.
Inelastic collision: Momentum conserved, KE NOT conserved. Coefficient of restitution e = 1 (elastic), e = 0 (perfectly inelastic — bodies stick together).
Perfectly inelastic: v_common = (m₁v₁ + m₂v₂)/(m₁+m₂). Maximum KE loss occurs in perfectly inelastic collision.
Kinetic: f_k = μ_k N
Always: μ_k < μ_s
Angle of repose: tan θ = μ_s
Incline: N = mg cos θ
KE = ½mv²
PE (gravity) = mgh
PE (spring) = ½kx²
W_net = ΔKE
Power P = W/t = Fv
v₁' = (m₁-m₂)v₁/(m₁+m₂) [if v₂=0]
v₂' = 2m₁v₁/(m₁+m₂)
Inelastic: v = (m₁v₁+m₂v₂)/(m₁+m₂)
e = 1 (elastic), e = 0 (perfectly inelastic)
a = (m₁-m₂)g/(m₁+m₂)
T = 2m₁m₂g/(m₁+m₂)
Net force = (m₁-m₂)g
Total mass = m₁+m₂
Work-energy: 1–2 Q/year
Collision: 1 Q/year
Atwood/connected bodies: 1 Q/year
Expected: Friction on inclined plane
Watch: Elastic collision velocity calculation