Physics 103 Equation Study Guide
Physics 103 Equations a2 + b2 = c2 If v = ∆x ¯ ∆t |g| = 9.8m/s2 1 K = 2 mv 2 Wnet = ∆K 2 |acent | = vtang /r ω = 2πf = 2π T sin θ = opposite hypotenuse
cos θ =
adjacent hypotenuse
tan θ = sin θ/ cos θ b x = −b± 2a −4ac v = v0 + at p = mv ¯ P =W t Wcons = −∆U P I = 4πr2 Fspr = −k ∆x √
2
ax2 + bx + c = 0 then 1 a = ∆v ¯ ∆t x = x0 + v0 t + 2 at2 Fext = ma = ∆p w = mg ∆t W =F s Ug = mgy ME = U + K M Ei + Wother = M Ef |τ | = rF⊥ v = fλ P = F/A Uspr = 1 kx2 2
1 4π 0
e = 1.6 × 10−19 C k= −27 mp = 1.67 × 10 kg Q 2 P E = Wext = U = 4π 10Q12 r −19 1eV = 1.6 × 10 J
= 8.99 × 109 N m2 /C 2 me = 9.11 × 10−31 kg Q ˆ F = qE F = 4π1 Qr22r 0 12 ∆V = ∆U/Q V = 4πQ0 r |E| |∆V | ∆s R = ρL A 1 Rpar−eq =
1 i Ri
I = ∆q j = I/A = nqvd ∆t P = IV Rser−eq = i Ri
∆V = IR ∆V = 0
Q C = ∆V Cparallel−plate = 0dA 1 1 Cpar−eq = i Ci i Ci Cser−eq = t V I(t) = Req e− τ Q(t) = Ceq V (1 − e−t/τ )
0
1 U = 1 CV 2 u = 2 0E 2 2 C = κe C τ = Req Ceq = 8.85 × 10−12 F/m
|F | = qvB⊥ |Bstraight−wire | =
µ0 I 2πr
|F | = IlB⊥ µ0 = 4π × 10−7 T m/A |Bloop−center | = µ0 I |Bsolenoid | = µ0 nI 2R = N ABω sin ωt 2 u = 1 B0 2µ
ΦB = B⊥ A = −N ∆ΦB = Blv ∆t N ΦB ∆I 1 L= I U = 2 LI 2 L = −L ∆t L τ = Req I(t) = Req (1 − e−t/τ ) I(t) = I0 e−t/τ eq
√ 2 Irms = Imax / 2 V (t) = Vmax sin ωt Prms = Irms R 1 XL = ωL XC = ωC c=
√1
0 µ0
Srms
= 2.998 × 108 m/s |E| = c|B| |S| = I = P/A = Erms Brms /µ0 Prad = I/c, 2I/c ∆p = ∆U/c
1
v = c/n θrefl = θinc |fspherical | = R/2 1 1 1 sin θcrit = n2 do + di = f n1 sin θ1 = n2 sin θ2 n1
hi m = ho = −di do n1 n2 n2 −n1 do + di = R
λn = λ/n δ = r2 − r1 δ = mλ, m = 0, 1, 2... δ = (m + 1 )λ, m = 0, 1, 2... 2 1 d sin θ = mλn , m = 0, 1, 2... d sin θ = (m + 2 )λn , m = 0, 1, 2... 1 2t = mλn , m = 0, 1, 2 2t = (m + 2 )λn , m = 0, 1, 2... a sin θ = mλn , m = 1, 2, 3... sin θ = 1.22λn /D R = Nm I = I0 cos2 θ γ=√
1 1−v 2 /c2
t = γt0
L = L0 /γ
E = mc2 = γm0 c2 E = m0 c2 + KE E 2 = p2 c2 + m2 c4 0 VCB +VAC VAB = VCB VAC
1+
c2
cos θ =
adjacent hypotenuse
tan θ = sin θ/ cos θ b x = −b± 2a −4ac v = v0 + at p = mv ¯ P =W t Wcons = −∆U P I = 4πr2 Fspr = −k ∆x √
2
ax2 + bx + c = 0 then 1 a = ∆v ¯ ∆t x = x0 + v0 t + 2 at2 Fext = ma = ∆p w = mg ∆t W =F s Ug = mgy ME = U + K M Ei + Wother = M Ef |τ | = rF⊥ v = fλ P = F/A Uspr = 1 kx2 2
1 4π 0
e = 1.6 × 10−19 C k= −27 mp = 1.67 × 10 kg Q 2 P E = Wext = U = 4π 10Q12 r −19 1eV = 1.6 × 10 J
= 8.99 × 109 N m2 /C 2 me = 9.11 × 10−31 kg Q ˆ F = qE F = 4π1 Qr22r 0 12 ∆V = ∆U/Q V = 4πQ0 r |E| |∆V | ∆s R = ρL A 1 Rpar−eq =
1 i Ri
I = ∆q j = I/A = nqvd ∆t P = IV Rser−eq = i Ri
∆V = IR ∆V = 0
Q C = ∆V Cparallel−plate = 0dA 1 1 Cpar−eq = i Ci i Ci Cser−eq = t V I(t) = Req e− τ Q(t) = Ceq V (1 − e−t/τ )
0
1 U = 1 CV 2 u = 2 0E 2 2 C = κe C τ = Req Ceq = 8.85 × 10−12 F/m
|F | = qvB⊥ |Bstraight−wire | =
µ0 I 2πr
|F | = IlB⊥ µ0 = 4π × 10−7 T m/A |Bloop−center | = µ0 I |Bsolenoid | = µ0 nI 2R = N ABω sin ωt 2 u = 1 B0 2µ
ΦB = B⊥ A = −N ∆ΦB = Blv ∆t N ΦB ∆I 1 L= I U = 2 LI 2 L = −L ∆t L τ = Req I(t) = Req (1 − e−t/τ ) I(t) = I0 e−t/τ eq
√ 2 Irms = Imax / 2 V (t) = Vmax sin ωt Prms = Irms R 1 XL = ωL XC = ωC c=
√1
0 µ0
Srms
= 2.998 × 108 m/s |E| = c|B| |S| = I = P/A = Erms Brms /µ0 Prad = I/c, 2I/c ∆p = ∆U/c
1
v = c/n θrefl = θinc |fspherical | = R/2 1 1 1 sin θcrit = n2 do + di = f n1 sin θ1 = n2 sin θ2 n1
hi m = ho = −di do n1 n2 n2 −n1 do + di = R
λn = λ/n δ = r2 − r1 δ = mλ, m = 0, 1, 2... δ = (m + 1 )λ, m = 0, 1, 2... 2 1 d sin θ = mλn , m = 0, 1, 2... d sin θ = (m + 2 )λn , m = 0, 1, 2... 1 2t = mλn , m = 0, 1, 2 2t = (m + 2 )λn , m = 0, 1, 2... a sin θ = mλn , m = 1, 2, 3... sin θ = 1.22λn /D R = Nm I = I0 cos2 θ γ=√
1 1−v 2 /c2
t = γt0
L = L0 /γ
E = mc2 = γm0 c2 E = m0 c2 + KE E 2 = p2 c2 + m2 c4 0 VCB +VAC VAB = VCB VAC
1+
c2