Dynamics

Cheat Sheet  ·  Physics Gr 11
Emil Oliversen
NEWTON'S LAWS
1st Law (Inertia)
ΣF = 0 → a = 0
Object stays at rest or constant velocity
2nd Law
ΣF = ma
x-axis
ΣFₓ = maₓ
y-axis
ΣFₔ = maₔ
Units: N = kg · m/s²
3rd Law (Action-Reaction)
FAB = −FBA
Equal magnitude, opposite direction, different objects
WEIGHT & NORMAL FORCE
Weight
Fg = mg   (g = 9.8 m/s²)
N (flat)
N = mg
N (incline)
N = mg cosθ
N ≠ mg on inclines! Always use mg cosθ.
ELEVATOR (APPARENT WEIGHT)
Accel. up
N = m(g + a)
Accel. down
N = m(g − a)
Free fall
N = 0 (weightless)
FREE-BODY DIAGRAM STEPS
  1. Isolate the object (dot or box)
  2. Draw all forces as arrows from centre
  3. Label each force (Fg, N, T, fk, Fapp)
  4. Choose + direction (right = +x, up = +y)
  5. Write ΣF = ma for each axis
  6. Solve for the unknown
TENSION
Massless rope: T is the same at every point
Tension pulls only — never pushes
Hanging (still)
T = Fg = mg
ATWOOD MACHINE
Two masses over frictionless pulley. m₂ > m₁ (m₂ falls)
Acceleration
a = (m₂−m₁)g / (m₁+m₂)
T (rising)
T = m₁(g + a)
T (falling)
T = m₂(g − a)
WORKED EXAMPLE
m₁ = 3 kg, m₂ = 5 kg
a = (5−3)(9.8)/(3+5) = 2.45 m/s²
T = 3(9.8+2.45) = 36.75 N
FRICTION
Static (max)
fs ≤ μsN   (not moving)
Kinetic
fk = μkN   (sliding)
μs > μk always
fk opposes direction of motion
μ has no units
INCLINED PLANE (angle θ)
Normal
N = mg cosθ
F‖ down slope
F‖ = mg sinθ
Kinetic friction
fk = μk mg cosθ
Accel. sliding
a = g(sinθ − μkcosθ)
Example: 10 kg on 30°, μk=0.2
N = 84.9 N   F‖ = 49 N
fk = 17 N   a = 3.2 m/s²
FRICTION WORKED EXAMPLE
15 kg box, Fapp=80 N, μs=0.45, μk=0.35
N = 147 N
Max static: 0.45×147 = 66.15 N < 80 N → slides
fk = 0.35×147 = 51.45 N
a = (80−51.45)/15 = 1.9 m/s²
PENDULUM FORCES
T acts along string toward pivot
mg acts downward
Net centripetal force = toward centre
General
T = mg cosθ + mv²/r
At rest (θ)
T ≈ mg cosθ
At bottom
T = mg + mv²/r
At bottom: T > mg always (must support weight + centripetal)
Example: 0.5 kg, v=2 m/s, r=0.8 m (bottom)
T = (0.5)(9.8) + (0.5)(4)/0.8
T = 4.9 + 2.5 = 7.4 N
COMMON MISTAKES
  • N ≠ mg on inclines — use mg cosθ
  • Friction opposes motion, not always leftward
  • Action-reaction pairs act on different objects
  • Tension pulls — never pushes
  • μ has no units (dimensionless)
  • Use μk once sliding, μs before sliding starts
  • Always draw FBD before writing equations
KEY FORMULA SUMMARY
ΣF = ma
Newton's 2nd Law
Fg = mg
Weight (g = 9.8 m/s²)
fk = μkN
Kinetic friction
N = mg cosθ
Normal on incline
a = g sinθ−μcosθ
Slide acceleration