Physics 1 - PHY 201/221

• PHY1&2 Toolbox / "Cheatsheet"

• PHY 201 Syllabus   -   Free Online Textbook

• PHY 221 Syllabus   -   Free Online Textbook:   Vol1   (don't need for 221, but also Vol2   Vol3)

• Practice Test Problems -  These are all worked in the "Practice Problems" videos in the links below, under each test material.

• Spreadsheet Graphing.pdf

• Kine HLab Data.pdf

• Vector HLab Data.pdf

Variables (units) 

F = Force (N) where 1 Newton = 1 N = 1 kg m / s

μ = coefficient of friction (none)

m = mass (kg)

weight = mg (N)

FN = “normal force” (N)

T = tension (N)

DHP = “downhill pull” (N)  = mg sin θ

FDRAG = ½ C A ρ v2 

Ff = force of friction (N) ≤ μ FN     (always)

    = μ m g                (on level surface if no other vertical forces)

    = μ m g cos θ      (on slope if no other vertical forces)

“Usual Suspects”: mg, FN , T, DHP, Ff , External/other

Formula

∑F = ma (Newton's 2nd Law)

Variables

W = work (J) where 1 Joule = 1J = 1 N m 

PE = potential/stored energy (J)

KE = kinetic/moving energy (J)

P = power (W) where 1 Watt = 1W = 1 J / s 

p = momentum (kg m / s2

J = impulse (N s)

k = spring constant (N/m)

e = coefficient of elasticity (none)

Formulas

W = F x            (Work if F ∥ x)            

    = F x cos ፀ     (Work if F ∦ x)

    = ∫ F dx    (Work if F not constant - Calculus/221 only)

PEGRAV = m g h     (Gravitational Potential Energy)

FSPRING = - k x     (Spring Force)

KE = ½ m v2     (Kinetic Energy)

PEGRAV = m g h     (Grav Potential Energy)

PESPRING = ½ k x2             (Spring Potential Energy)

W = ΔE = ΔKE + ΔPE    (work-energy theorem)

Cons of Energy: E1 = E2       (1 obj @ 2 points) 

    usually ½ m v12 + m g h1 = ½ m v22 + m g h2 

p = m v (Momentum)

J = Δp or  F t = m v2 - m v1 (impulse-momentum theorem)

Cons of Mom: p = p’     (2 objs collide) 

always m1 v1 + m2 v2 = m1 v1’ + m2 v2’ 

Special Cases: 

If inelastic/ hit&stick

v’ = (m1 v1 + m2 v2) / (m1 + m2 ) 

If elastic/ hit&bounce

v1’ = (m1 - m2 ) v1 / (m1 + m2 ) + 2m2  v2 / (m1 + m2 )      

v2’ = 2m1 v1 / (m1 + m2 ) - (m1 - m2 ) v2 / (m1 + m2 )      

If neither perfectly elastic or inelastic

e = √(h’ / h)          (object dropped from height h)   

e = (v2’ - v1’) / (v1 - v2)      (two colliding objects)

Calculus Formulas - 221 only

W = ∫ F dx

F = dp / dt

J = ∫ F dt

Variables

ፀ = theta = angle (rad)    (replaces x, where x = r ፀ) 

ω = omega = angular velocity (rad/s)    (replaces v, where v = r ω)

∝ = alpha = angular acceleration (rad/s2)    (replaces a, where a = r ∝)

I = moment of inertia (kg m2)   (replaces m)

τ = tau = torque (aka moment) (Nm)    (replaces F)

Formulas

ω = Δፀ / ΔT      (Angular Velocity)

∝ = Δω / ΔT (Angular Acceleration)

ac = v2 / r        (Centripetal Acceleration)

Fc = m v2 / r    (Centripetal Force)

FG = G m1 m2 / r2    (Gravitation)

T12 / R13 = T22 / R23    (Kepler's 3rd Law)

I = Σ mi ri2     (see table for shapes)

tan ፀ = v2 / g r    (bank angle)

Linear/Old Angular/Rotational/New

v = vO + a t ω = ωO + ∝ t

x = vO t + ½ a t 2 ፀ = ωO t + ½ ∝ t 2

v2 = vO2 + 2 a x ω2 = ωO2 + 2 ∝ ፀ

F = m a τ = I ∝

KE = ½ m v2 KEROT = ½ I ω2

p = m v   L = I ω 

Variables

τ = tau = torque (aka moment) (Nm) 

ρ = density (kg/m3)

P = Pressure (Pa, where 1 Pa = 1 N / m2)

V = Volume (m3)

v = Velocity (m/s)

A = Area (m2)

L = Length (m)

η = Viscosity (eta)

R = Rate of Flow (m3 / s)

NR = Reynolds Number 

Formulas

Statics

ΣF = 0

Στ = 0

Fluid Statics

ρ = m / V (Density)

SG = ρobj / ρH2O     (Specific Gravity)

P = F / A (Pressure)

PDepth = ρ g h (Pressure at depth/Gauge Pressure)

PABS = PGauge + PATM (Absolute Pressure)

FB =  ρFluid g VDisp      (Buoyant Force)

Hydraulics

F1 / A1 = F2 / A2  

A1 L1 = A2 L2

Fluid Dynamics

A1 v1 = A2 v2    (Eq of continuity)

p1 + ρ g h1 + ½ ρ v12 = p2 + ρ g h2 + ½ ρ v22   (Bernoulli’s Eq) 

v = √(2 g h)    (Torricelli's Theorem)

 k         h          da        -          d         c          m     

kilo    hecto   deca    none    deci    centi     milli 

Order of Operations

      Parentheses

      Exponents

      Multiplication & Division

      Addition & Subtraction

Αα   Alpha   Νν   Nu

Ββ   Beta         Ξξ   Xi

Γγ   Gamma       Οο   Omicron

Δδ   Delta   Ππ   Pi

Εε   Epsilon        Ρρ   Rho

Ζζ   Zeta           Σσ   Sigma

Ηη   Eta              Ττ   Tau

Θθ   Theta   Υυ   Upsilon

Ιι   Iota           Φφ   Phi

Κκ   Kappa   Χχ   Chi

Λλ   Lambda       Ψψ   Psi

Μμ   Mu           Ωω   Omega

√ ≠  ≥ ≤   ≈ ± ∥ ∩ ∪ ∈ ⇒ ∴ ∫ ∮ ⋅