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A 4 kg block sits on a 30° incline. What's the normal force?
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Maria Santos
MIT · Mechanical Engineering, Year 3
Worst grade: C+ in Statics (freshman year)"I failed the first midterm because I kept mixing up normal force and weight. Now I draw every single problem before I solve it."
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FBD Shorthand
N = mg·cos θ
f = μN
ΣF = ma → always!
Incline Rules
x-axis: along slope
y-axis: ⊥ to slope
Never forget the angle!
Joaquin Reyes
Caltech · Physics, Year 2
Worst grade: D in E&M (sophomore year)"Dimensional analysis saved my GRE score. I was failing practice tests until I built this flow — now I catch errors in 10 seconds."
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DA Cheat Flow
[Force] = kg·m/s²
[Energy] = kg·m²/s²
Check before solving!
SI Prefixes
μ = 10⁻⁶
n = 10⁻⁹
G = 10⁹
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Priya Krishnamurthy
Georgia Tech · EE, Year 3
Worst grade: C in Electricity & Magnetism (Year 2)"Every textbook derivation of Gauss's Law felt like it was hiding something. I wrote this for myself first — then 400 people saved it."
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Gauss's Law
∮E·dA = Q_enc/ε₀
Symmetry is the key
3 geometries only
E-field table
Sphere: kQ/r²
Cylinder: λ/2πε₀r
Plane: σ/2ε₀
Devon Williams
UT Austin · Aerospace Eng., Year 2
Worst grade: C- in Dynamics (Year 1)"Torque finally clicked when I stopped thinking about formulas and started thinking about doors. That's the mental model in my notes."
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Torque Intuition
τ = r × F
Perpendicular = max
Think: door hinge!
Moment of Inertia
I = Σmr²
Parallel axis: I+md²
Rod tip: mL²/3
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Projectile Motion
KinematicsHorizontal velocity stays constant. Vertical acceleration = g downward. Solve x and y independently.
Newton's 2nd Law
Energy Conservation
KE + PE = const
½mv² + mgh = E
No friction → exact
Torque
τ = rF sinθ
τ = Iα
Max when θ = 90°
Gauss's Law
∮ E · dA = Q_enc / ε₀
"Pick your surface so E is constant — sphere for point charge, cylinder for wire." — Priya K.
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