The Simple AP Physics C Mechanics Cheat Sheet

The Simple AP Physics C Mechanics Cheat Sheet

AP Physics C Mechanics Cheat Sheet provides essential formulas and concepts for mastering mechanics in the AP Physics C exam. It covers kinematics, forces, energy, momentum, and rotational dynamics, making it a valuable resource for students preparing for the May exam. This cheat sheet includes key equations, problem-solving strategies, and graphical interpretations to enhance understanding. Ideal for AP Physics students looking to review critical topics and improve their exam performance.

Key Points

  • Covers kinematics equations including projectile motion and relative velocity.
  • Explains Newton's laws of motion and free body diagrams for analyzing forces.
  • Includes work-energy principles and calculations for both conservative and non-conservative forces.
  • Details linear momentum concepts, including impulse and conservation during collisions.
  • Describes rotational dynamics, including torque, moment of inertia, and angular momentum.
  • Provides insights into oscillations, including simple harmonic motion and energy conservation.
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The Simple AP Physics C: Mechanics Cheat Sheet
1: Kinematics (10–15%)
Calculus kinematics & graphs
Derivatives: v = dx/dt, a = dv/dt; integrals reverse: x
= ∫v dt.
Constant a: v-t linear, x-t parabolic. Variable a →
integrate.
Slopes: slope x-t = v; slope v-t = a. Areas: under v-t =
Δx.
Equation selection
Known Missing Use
v₀, v, Δx t v² = v₀² + 2aΔx
v₀, a, t Δx v = v₀ + at
v₀, a, Δx v Δx = v₀t + ½at²
Projectile motion (2D)
Independence: x & y axes separate; solve each, link
by t.
Components: v₀ₓ = v₀ cos θ (const); v₀y = v₀ sin θ
(−g).
Range = v₀² sin(2θ)/g, max @ 45°. T = 2v₀ sin θ/g.
Max height: set vy = 0 → h = v₀² sin²θ/(2g).
⚠
TRAP: vy reverses after peak; speed at landing ≠
v₀ if heights differ.
Relative velocity
Frame rule: vA/B = vA − vB; chain rule for 3+ frames.
River: aim ⊥ → shortest path (diagonal); upstream →
straight.
Non-inertial: accelerating frame → pseudo-forces
appear.
✓
TIP: Define frame & +direction first; label all
velocities.
2: Force & Translational Dyn. (20–25%)
FBD & Newton's laws
FBD: isolate object → draw all forces (W, N, f, T) →
resolve x, y.
Newton's 2nd: ΣFₓ = maₓ, ΣFy = may; solve
simultaneously.
Newton's 3rd: FAB = −FBA; same magnitude, diff.
objects.
Circular: ΣF toward center = mv²/r; it's the net force,
not extra.
Common force relationships
Force Key relationship
Static friction f
ₛ
≤ μ
ₛ
N (adjusts)
Kinetic friction f
ₖ
= μ
ₖ
N (constant)
Normal N ≥ 0, always ⊥
Tension same T (massless)
Spring F = −kx (restoring)
Inclined planes
Weight decomp: mg sin θ ∥ ramp; mg cos θ ⊥ ramp.
No-slip: f
ₛ
= mg sin θ; slides when tan θ > μ
ₛ
.
Sliding: a = g(sin θ − μ
ₖ
cos θ).
Multi-body systems
Atwood: a = (m₁ − m₂)g/(m₁ + m₂); T = 2m₁m₂g/(m₁ +
m₂).
Massless string: same |a| & T throughout rope.
Constraint: string length const → link accelerations.
Drag: terminal v when drag force = mg.
⚠
CRITICAL: T ≠ mg; find T from ΣF = ma / object.
Count unknowns vs. equations; constraints fill gaps.
3: Work, Energy & Power (15–25%)
Work calculation
Constant F: W = FΔx cos θ; variable F: W = ∫F·dx.
Wnet = ΔKE = ½m(vf² − vᵢ²); fastest speed-change
method.
Zero work: F ⊥ motion → W = 0 (normal, centripetal
T).Gravity: Wg = −mgΔh; friction: Wf = −f
ₖ
d (always
neg.).
Conservative forces & PE
Type Path-dep? Examples
Conservative No gravity, spring
Non-conserv. Yes friction, drag
PE curves: F = −dU/dx; force points downhill on U(x).
Equi.: dU/dx = 0. Stable = U min; unstable = U max.
Energy conservation
No friction: KEᵢ + PEᵢ = KEf + PEf; set h = 0 wisely.
With friction: KEᵢ + PEᵢ − f
ₖ
d = KEf + PEf.
Spring PE = ½kx²; gravity PE = mgh (ref. pt.
matters).Energy bar charts: sketch KE + PE bars
before/after to track flow.
System: include Earth → use PE; excl. → extern. Wg.
Power
Instantaneous: P = dW/dt = Fv cos θ; avg: Pavg =
ΔE/Δt.Efficiency: η = Pout/Pin; always < 1 w/
friction.Area under F-x = work by variable force
(graphical method).KE = ½mv² (always +); Wnet =
ΔKE links force to motion.
⚠
Speed changes w/o work? F must be
⊥
motion.
✓
TIP: Speed → energy. Need accel. → F = ma.
4: Linear Momentum (10–20%)
Momentum & impulse
Momentum: p = mv; impulse: J = FavgΔt = Δp.
Calculus: J = ∫F dt; area under F-t graph = impulse.
Airbag: ↑ Δt → ↓ Favg for same Δp (reduces force).
Setup: draw before/after; separate pₓ & py if 2D.
Collision types
Type KE saved? Approach
Elastic Yes p + KE (2 eqs)
Inelastic No p only
Perfectly inel. No (max) p → common vf
Conservation workflow
Condition: ΣFext ≈ 0 during event → Σpᵢ = Σpf.
Perfectly inel.: m₁v₁ + m₂v₂ = (m₁ + m₂)vf.
Recoil: pᵢ = 0 → m₁v₁ = −m₂v₂ (explosion).
Equal mass 1D elastic: velocities exchange.
2-body elastic: use both p & KE eqs → 2 unknowns,
2 eqs.
Center of mass & 2D
CM: xcm = Σmᵢxᵢ/M; vcm = ptotal/M.
CM motion: ΣFext = Macm; Fext = 0 → CM const. v.
Ballistic pend.: momentum first → energy (swing).
2D: conserve pₓ & py separately; need angle info.
Impulse approx.: short Δt → only internal forces
matter.Rocket: thrust = vexhaust × (dm/dt); p
changes w/ mass.KE loss: max in perfectly inel.;
check ΔKE = KEf − KEᵢ.
⚠
CRITICAL: Define system; check if ext. forces act.
✓
TIP: Draw p vectors before/after; use CM for
elastic.
5: Torque & Rotational Dynamics (10–15%)
Torque basics
Torque: τ = rF sin θ = rF⊥; use lever arm form.
Right-hand rule: curl r to F → thumb = τ direction.
Rot. Newton's 2nd: Στ = Iα; τ & I same axis.
I = Σmᵢrᵢ² or ∫r²dm; mass far from axis → bigger I.
Moment of inertia
Shape Axis I
Disk/cyl. center ½MR²
Hoop center MR²
Sphere center
⅖
MR²
Rod (center) center ¹⁄₁₂ML²
Rod (end) end ⅓ML²
Parallel axis shifted Icm + Md²
Rotational kinematics
Analogs: θ↔x, ω↔v, α↔a; same kinematic eqs.
Key: ωf = ωᵢ + αt; ωf² = ωᵢ² + 2αΔθ.
Rolling: vcm = ωR, acm = αR (no-slip constraint).
α = Στ/I; combine w/ rot. kinematics for ω, θ.
Static equilibrium
Conditions: ΣFₓ = 0, ΣFy = 0, Στ = 0 (any axis).
Pivot trick: axis at unknown → that torque = 0.
Beam: Στ about one support → find the other.
Sign: CCW = + (standard); stay consistent.
Units: N·m for torque ≠ J for energy (same dim.).
⚠
TRAP: Forgot Md² in parallel axis theorem?
✓
TIP: Pick pivot to eliminate unknowns.
6: Rotating Systems (10–15%)
Rotational KE & work
KErot = ½Iω²; rolling: KEtot = ½mvcm² + ½Iω².
Shortcut: KE = ½mvcm²(1 + I/(mR²)); shape factor.
Work: W = τΔθ; power: P = τω (watts).
Energy cons.: mgh = ½mvcm² + ½Iω² (rolling ramp).
Rolling race
Shape I/(mR²) Rank
Solid sphere 2/5 fastest
Solid cylinder 1/2 2nd
Hollow sphere 2/3 3rd
Hoop 1 slowest
Why? More I → more KE in rotation → less
translation → slower.
Angular momentum
L = Iω (axis); L = mvr sin θ (point particle).
Conservation: Στext = 0 → Lᵢ = Lf. Skater: I↓ → ω↑.
Impulse: τΔt = ΔL = I(ωf − ωᵢ).
Stick collision: L about pivot conserved; check KE.
Wrot = τΔθ; use for torque doing work over angle.
Rolling friction
Rolling f: gives torque, does no work (contact pt. still).
Slip → roll: friction until vcm = ωR; use ΣF & Στ.
Precession: spinning top + gravity τ → L traces cone.
Particle L: L = mvr⊥; use for orbits & off-axis hits.
⚠
CRITICAL: Rolling → BOTH ½mvcm² + ½Iω²
needed.
✓
TIP: L avoids forces; use when Στext = 0.
7: Oscillations (10–15%)
SHM kinematics
SHM test: F ∝ −x → a = −ω²x (d²x/dt² + ω²x = 0).
Position: x = A cos(ωt + φ); velocity: v = −Aω sin(ωt
+ φ).
Maxima: |v|max = Aω (x = 0); |a|max = Aω² (x = ±A).
Period: T = 2π/ω = 2π√(m/k); indep. of amplitude.
Energy in SHM
Position KE PE
x = ±A 0 ½kA²
x = 0 ½kA² 0
any x ½mv² ½kx²
Speed: v = ω√(A² − x²); total E = ½kA² (constant).
Initial conditions
General: A = √(x₀² + (v₀/ω)²); tan φ = −v₀/(ωx₀).
From rest at x₀: A = |x₀|; φ = 0 or π.
From equil.: A = v₀/ω; φ = ±π/2.
Pendulums & springs
Simple pend.: T = 2π√(L/g); small angle only.
Physical pend.: T = 2π√(I/(mgd)); d = pivot to CM.
Springs: parallel k = k₁+k₂; series 1/k = 1/k₁+1/k₂.
Vertical spring: equil. shifts mg/k; ω unchanged.
Damping & resonance
Damped: A decays; ωd < ω₀. Critical: fastest return.
Resonance: max A at fdrive ≈ fnat; width ∝ damping.
⚠
TRAP: φ sign — check t = 0 in x(t) & v(t).
✓
TIP: At extreme → energy. Need x(t) → A
cos(ωt+φ).
Cross-Cutting Strategies & FRQ Tips
FRQ framework
(a) Setup: system, diagram (FBD/energy/p), label
vars.
(b) Equation: ΣF = ma, Eᵢ = Ef, pᵢ = pf, or Στ = Iα.
(c) Algebra: symbolic first; numbers at end.
(d) Justify: why method works; check units.
Method selection
Find… Method Why
Speed (fall) Energy no forces
Tension ΣF = ma a known
vf (collision) Momentum E unknown
ω τ = Iα or L torques given
Amplitude Energy ½kA² = E
Common pitfalls
Signs: PE = +mgh; p < 0 if opp. to + direction.
Units: radians in ω, α, SHM; g = 9.8 m/s².
Trig: watch √2, √3; keep exact until final step.
Stuck on (a)? Use symbol in (b); method earns credit.
MC & time tips
MC: eliminate 2 → guess remaining; ~2 min/Q.
FRQ: skim all 4 first; start w/ easiest.
Partial credit: method > final answer for graders.
Reasonableness: v ≈ 10–30 m/s; check magnitude.
Dimensional analysis: if units don't match, answer is
wrong.
⚠
CRITICAL: Show all work; method > final number.
✓
TIP: Stuck? Use prior answer as variable & keep
going.
AP Physics C: Mechanics — 80 min MC (40 Qs, 4 choices) + 100 min FRQ (4 Qs). MC 50%, FRQ 50%. Equation sheet provided. Calculator allowed. | www.albert.io
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FAQs of The Simple AP Physics C Mechanics Cheat Sheet

What kinematics concepts are included in the AP Physics C Mechanics Cheat Sheet?
The AP Physics C Mechanics Cheat Sheet includes essential kinematics concepts such as the equations of motion for constant acceleration, projectile motion analysis, and the independence of motion in two dimensions. It emphasizes the importance of understanding velocity and acceleration graphs, as well as the relationships between displacement, velocity, and time. Students can find formulas for calculating maximum height, range, and time of flight for projectiles, which are critical for solving exam problems.
How does the cheat sheet explain Newton's laws of motion?
Newton's laws of motion are clearly outlined in the cheat sheet, providing students with a foundational understanding of classical mechanics. The first law describes inertia and the concept of a net force, while the second law relates force, mass, and acceleration through the equation F=ma. The third law emphasizes action-reaction pairs, illustrating how forces interact between objects. Additionally, the cheat sheet includes free body diagram techniques for visualizing forces acting on an object, which is crucial for problem-solving.
What energy concepts are covered in the AP Physics C Mechanics Cheat Sheet?
The cheat sheet covers key energy concepts, including work, kinetic energy, and potential energy. It explains how work done by a force relates to changes in kinetic energy through the work-energy theorem. Additionally, it discusses conservative forces, such as gravity and springs, and how they affect potential energy. Students will find formulas for calculating gravitational potential energy and spring potential energy, along with examples of energy conservation in closed systems.
What topics related to linear momentum are included in the cheat sheet?
Linear momentum topics in the cheat sheet include the definition of momentum as the product of mass and velocity, as well as the principle of conservation of momentum during collisions. It distinguishes between elastic and inelastic collisions, detailing how kinetic energy is conserved in elastic collisions but not in inelastic ones. The cheat sheet also covers impulse and its relationship to momentum, providing students with the tools to analyze various collision scenarios effectively.
How does the cheat sheet address rotational dynamics?
Rotational dynamics are addressed through key concepts such as torque, moment of inertia, and angular momentum. The cheat sheet provides formulas for calculating torque based on force and lever arm distance, as well as the moment of inertia for various shapes. It explains the rotational analogs of Newton's second law, linking torque to angular acceleration. Students will also learn about the conservation of angular momentum and its applications in rotational motion problems.
What oscillation topics are included in the AP Physics C Mechanics Cheat Sheet?
The cheat sheet includes topics related to oscillations, particularly simple harmonic motion (SHM). It outlines the characteristics of SHM, such as the relationship between force and displacement, and provides formulas for calculating the period and frequency of oscillating systems. The energy in SHM is discussed, detailing how potential and kinetic energy interchange during motion. Additionally, the cheat sheet covers damping and resonance, explaining how these phenomena affect oscillatory systems.

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