The Simple AP Physics C Mechanics Cheat Sheet

The Simple AP Physics C Mechanics Cheat Sheet

The Simple AP Physics C Mechanics Cheat Sheet serves as an essential resource for students preparing for the AP Physics C exam. It covers key concepts in mechanics, including kinematics, forces, work, energy, momentum, and rotational dynamics. This cheat sheet provides formulas, definitions, and problem-solving strategies tailored for AP Physics C students. It is designed to help learners quickly review critical topics and enhance their understanding of complex physics principles. Ideal for exam preparation, this guide streamlines the study process and aids in mastering challenging concepts.

Key Points

  • Covers kinematics, including equations of motion and projectile motion principles.
  • Explains Newton's laws of motion and their applications in various scenarios.
  • Includes work-energy principles and calculations for both conservative and non-conservative forces.
  • Details linear momentum concepts, including impulse and conservation during collisions.
  • Discusses rotational dynamics, including torque, moment of inertia, and angular momentum.
  • Provides strategies for solving multi-body systems and analyzing forces on inclined planes.
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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 are the main topics covered in the AP Physics C Mechanics Cheat Sheet?
The AP Physics C Mechanics Cheat Sheet covers essential topics such as kinematics, forces, work and energy, linear momentum, and rotational dynamics. Each section provides key formulas and concepts necessary for understanding mechanics at an advanced level. Students can find detailed explanations of projectile motion, Newton's laws, and energy conservation principles. Additionally, the cheat sheet addresses torque and angular momentum, which are crucial for mastering rotational dynamics.
How does the cheat sheet assist with exam preparation for AP Physics C?
The cheat sheet is designed to streamline the study process for AP Physics C students by summarizing critical concepts and formulas in a concise format. It allows students to quickly reference key equations and principles, making it easier to review before the exam. By providing clear explanations and problem-solving strategies, the cheat sheet helps students reinforce their understanding of complex topics and improve their performance on the AP exam.
What formulas are included in the mechanics section of the cheat sheet?
The mechanics section of the cheat sheet includes important formulas related to kinematics, such as the equations of motion for constant acceleration. It also features Newton's second law, work-energy theorem, and formulas for calculating momentum and impulse. For rotational dynamics, the cheat sheet provides equations for torque, moment of inertia, and angular momentum. These formulas are essential for solving problems and understanding the underlying principles of mechanics.
What is the significance of understanding work and energy in physics?
Understanding work and energy is crucial in physics as it lays the foundation for analyzing how forces affect motion. The work-energy principle states that the work done on an object is equal to the change in its kinetic energy, which helps in solving various mechanics problems. Additionally, recognizing the difference between conservative and non-conservative forces allows students to apply energy conservation principles effectively. Mastery of these concepts is vital for success in AP Physics C and real-world applications.
How does the cheat sheet explain rotational dynamics?
The cheat sheet explains rotational dynamics by introducing key concepts such as torque, moment of inertia, and angular momentum. It outlines how torque is calculated and its role in causing rotational motion. The moment of inertia is discussed in relation to different shapes and how it affects rotational acceleration. Furthermore, the cheat sheet emphasizes the conservation of angular momentum, illustrating its importance in various physical systems, such as spinning objects and collisions.

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