Physics 111 Common Exam 3 Formulasfederici/Phys111/exams/Exam3_formula-sheet.pdfPhysics 111 Common...
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Page 6 of 7 6 Physics 111 Common Exam 3 Formulas Conversion Factors: 1 inch = 2.54 cm; 1 mi =1609.3 m; 1 cm=10 -2 m; 1 mm= 10 -3 m; 1 g=10 -3 kg; Physical constants: 9.8 g = m/s 2 ; 11 6.674 10 G − = × N m 2 /kg 2 ; 24 5.97 10 Earth M = × kg ; 6 6.37 10 Earth R = × m Math: 360° = 2π radians = 1 revolution. Arc length s r θ = ; 3 4 /3 sphere V R π = ; 2 4 sphere A R π = ; 2 circle A R π = quadratic formula to solve 2 0 ax bx c + + = : 2 4 2 b b ac x a − ± − = Vectors: A x = A cosθ; A y = A sinθ; A = 2 y 2 x A A + ; θ = tan -1 x y A A ; A = A x î + A y ĵ A + B = C ⇒ C x = A x + B x , C y = A y + B y ; y y x x B A B A cos | B || A | B A + = θ = ⋅ ; One-dimensional motion: x = v avr t ; x = x 0 + v o t + 1 2 at 2 , a 2 v v x 2 0 2 − = ; v = v o + at; t 2 v v x 2 1 + = ; Free-fall: y =y 0 + v o t - 2 1 gt 2 , v = v o - gt, g 2 v v y 2 o 2 − − = ; g 2 v y 2 0 max = g 2 v t y 0 tot = Two-dimensional motion: r = r 0 + (v ox t + 1 2 a x t 2 ) î + (v oy t + 1 2 a y t 2 ) ĵ v = (v ox + a x t) î + (v oy + a y t) ĵ; Projectile motion: x = v ox t ; y = v 0y t - 1 2 gt 2 ; v y = v oy - gt; v ox = v o cosθ; v oy = v o sinθ; g 2 v v y 2 oy 2 y − − = ; Range = ; g 2 sin v 2 o θ 2 0 2 ) cos v ( 2 gx x ) (tan y θ − ⋅ θ = g 2 v y 2 oy max = g 2 v 2 t oy tot = Circular motion: a c = R v 2 ; period T = v R 2π ; Dynamic: F net = ma; F netx = ma x ; F nety = ma y ; |F g | = mg, ; g = 9.8 m/s 2 ; F net = r mv 2 ; Incline: F gx (along an incline) = mgsinθ F gy (perpendicular to an incline) = mgcosθ work: W = F ⋅ d = Fdcosφ; W mg = mg(y 0 - y) , F spring = -kx ; W spring = 1 / 2 k(x 0 2 -x 2 ) W fr = -F k d; F k = µ k N; W tot = K f - K i ; P avg = t W ∆ P = F Kinetic energy: K = m 2 1 v 2 U g = mg(y-y 0 ) U s = 1 / 2 kx 2 , U gi + U si + K I = U gf + U sf + K f U gi + U si + K I + W nc = U gf + U sf + K f momentum: p = mv; P i = P f ; m 1 v i1 + m 2 v i2 = m 1 v f1 + m 2 v f2 ; F net ∆t = mv f - mv i elastic: 2 2 1 1 2 1 2 1 1 ' 2 2 2 1 2 1 2 1 2 1 ' 1 2 ; 2 v m m m m v m m m v v m m m v m m m m v + − + + = + + + − = , perf. inelastic: m 1 v i1 + m 2 v i2 = (m 1 + m 2 ) V
Transcript of Physics 111 Common Exam 3 Formulasfederici/Phys111/exams/Exam3_formula-sheet.pdfPhysics 111 Common...
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Physics 111 Common Exam 3 Formulas Conversion Factors: 1 inch = 2.54 cm; 1 mi =1609.3 m; 1 cm=10-2 m; 1 mm= 10-3 m; 1 g=10-3 kg; Physical constants: 9.8g = m/s2 ; 116.674 10G −= × N m2/kg2 ; 245.97 10EarthM = × kg ; 66.37 10EarthR = × m Math: 360° = 2π radians = 1 revolution. Arc length s rθ= ; 34 / 3sphereV Rπ= ; 24sphereA Rπ= ; 2
circleA Rπ=
quadratic formula to solve 2 0ax bx c+ + = : 2 4
2b b acx
a− ± −
=
Vectors: Ax = A cosθ; Ay = A sinθ; A = 2y
2x AA + ; θ = tan-1
x
y
AA
; A = Ax î + Ayĵ
A + B = C ⇒ Cx = Ax + Bx , Cy = Ay + By; yyxx BABAcos|B||A|BA +=θ=⋅ ;
One-dimensional motion: x = vavrt ; x = x0 + vot +12
at2, a2vv
x2
02 −
= ; v = vo + at; t2
vvx 21 +
= ;
Free-fall: y =y0 + vo t -21
gt2, v = vo - gt, g2vv
y2
o2
−−
= ; g2
vy
20
max = g2
vt y0tot =
Two-dimensional motion: r = r0 + (vox t +12
ax t2) î + (voy t +12
ay t2) ĵ v = (vox + ax t) î + (voy + ayt) ĵ;
Projectile motion: x = voxt ; y = v0yt - 12
gt2; vy = voy - gt; vox = vocosθ; voy = vosinθ; g2vv
y2
oy2
y
−
−= ;
Range = ;g
2sinv 2o θ
20
2
)cosv(2gxx)(tany
θ−⋅θ=
g2v
y2
oymax =
g2v2
t oytot = Circular motion: ac =
Rv2
; period T = vR2π ; Dynamic: Fnet = ma; Fnetx = max ; Fnety = may; |Fg| = mg, ; g = 9.8 m/s2;
Fnet = r
mv2
;
Incline: Fgx(along an incline) = mgsinθ Fgy(perpendicular to an incline) = mgcosθ
work: W = F ⋅ d = Fdcosφ; Wmg = mg(y0 - y) , Fspring = -kx ; Wspring = 1/2 k(x02 -x2)
Wfr = -Fk d; Fk = µkN; Wtot = Kf - Ki ; Pavg = t
W∆
P = F Kinetic energy: K = m21 v2
Ug = mg(y-y0) Us = 1/2 kx2, Ugi + Usi + KI = Ugf + Usf + Kf Ugi + Usi + KI + Wnc = Ugf + Usf + Kf
momentum: p = mv; Pi = Pf ; m 1vi1 + m2vi2 = m1vf1 + m2vf2 ; Fnet ∆t = mvf - mvi
elastic: 221
121
21
1'22
21
21
21
21'1
2;2 vmmmmv
mmmvv
mmmv
mmmmv
+−
++
=+
++−
= , perf. inelastic: m 1vi1 + m2vi2 = (m 1 + m2) V
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212211
com mmxmxm
x++
= 21
221com mm
vmmvv
++
= 1m = 100 cm = 1000 mm 1 hour = 60 min = 3600 sec.
Rcom = iirmM1
Σ vcom= iivmM1
Σ
360° = 2π radians = 1 revolution. s = rθ vt = rω at = rα ac = ar =vt
2/r = ω2r atot2 = ar
2 + at2
ω = ωo + αt θf − θo = ωot +½αt2 ωf2 − ωo
2 = 2α(θ − θo) θ − θo = ½(ω+ ωo)t Krot = 1/2Iω2 I = Σmiri2
Ipoint = mr2 Ihoop = MR2 Idisk = 1/2 MR2 Isphere = 2/5 MR2 Ishell = 2/3 MR2 Irod (center) = 1/12 ML2 Irod (end) = 1/3 ML2
τ = force×moment arm = F⋅r⋅sin(φ) τnet = Στ= Ι α Fnet = ΣF = m a τ = r x F Ip = Icm + Mh2
Wtot = ∆K = Kf − KI W = τnet∆θ K = Krot + Kcm Emech = K + U Paverage = ∆W/∆t
Pinstantaneous = τ⋅ω (for τ constant) ∆Emech= 0 (isolated system) vcom = ωr (rolling, no slipping) l = r x p p = mv L = Σ li τnet = dL/dt L = Iω lpoint mass = m⋅r⋅v⋅sin(φ)
For isolated systems: τnet = 0 L is constant ∆L = 0 L0 = Σ I0ω0 = Lf = Σ Ifωf
