# 250+ Physics Formulas Most commonly Used

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Measurements

1.      Smallest unit of measurement by;

Measurement tape → 1 cm or 1mm

Meter rule or half meter rule → 0.1 cm or 1 mm

Vernier caliper → 0.01 cm or 0.1 mm

Screw gauge → 0.001 cm or 0.01 mm

2.      θ = s/r

4.      3600 = 1 revolution

6.      1 degree = 60 minute

7.      1 minute = 60 seconds

8.      Angle at circle is 2π radian.

9.      Angle at sphere is 4π steradian.

10.  Volume of slid cylinder = πr2l

11.  Area of sphere = 4πr2

12.  Volume of sphere = 4/3 πr3

13.  Dimension of velocity = [LT-1]

14.  Dimension of acceleration= [LT-2]

15.  Energy of photon; E = hf

16.  Time period of pendulum; T = 2π

Vectors and equilibrium

17.  Commutative property of vector= A+B = B+A

18.  Fx =F cosθ

19.  Fy = Fsinθ

20.  F =

21.  A.B = AB cos θ

22.  A x B = AB sin θ

23.  Scalar product; work and power

24.  Vector product; torque

25.  τ = r x F

26.  First condition of equilibrium; ∑F = 0

27.  Second condition of equilibrium; ∑τ = 0

Motion and Force

28.  v = s/t

29.  a = v/t

30.  vf = vi +at

31.  s = vit + ½ at2

32.  2as = vf2 – vi2

33.  S = vave x t

34.  Vave 🙁 vi + vf )/2

35.  g = 9.8 ms-2 = 32 ft-2

36.  F = ma

37.  a = v/t

38.  P = mv

39.  P = F t

40.  Impulse; J = F x t = ∆P

41.  J = ∆P

42.  Law of conservation of momentum; ∆p = 0

43.  Elastic collision in one dimension; [v1 + v2] = [v1’+ v2’]

44.  Magnitude of projectile velocity; Vf =

45.  Height of projectile; H = vi2sin2θ/2g

46.  Time of flight; T = 2 vi sinθ/g

47.  Time of summit or time to reach to highest point; T = vi sinθ/g

48.  Range; R = vi2 sin 2θ/g

49.  Rmax = vi2/g

50.  R = Rmax at 450

Work and Energy

51.  W = Fd cosθ

52.  Power; p=W/t or p =Fv

53.  1 watt = Js-1

54.  1 hp = 746 watts

55.  K.E = ½ mv2

56.  P.E = mgh

57.  Efficiency = output/input = W x D/P x d

58.  Absolute potential energy =Fr = - GmMe/Re (- because work is done against gravity)

59.  Gravitational potential = E/m = GMe/Re

60.  For escape velocity compare K.E with Absolute potential energy; vesc =  → vesc =

61.  G = 6.67 x 10-11 Nm2kg-2

62.  Re = 6.4 x 106 m

63.  Me = 6 x 1024 kg

64.  Vesc = 11.2 x 103 ms-1

65.  Wh = K.E + fh → (Wh = loss in potential energy)

66.  Loss in P.E = Gain inn K.E + work done against friction

67.  E = mc2 →(c= 3 x 108 ms-1)

Rotational and circular motion

68.  Angular velocity; ω = ∆θ/∆t

69.  Angular acceleration; α = ∆ω/∆t → a = α x r

70.  v = r ω

71.  Fc = mv2/r

72.  ac = -(v2/r)

73.  Centrifugal force= mv2/r

74.  F sin θ = mv2/r

75.  F cos θ = mg

76.  Tan θ = v2/gr

77.  Τorque = r F = rma = rm (rα) 🙁 r2m)α = I α

78.  Moment of inertia; I = mr2

79.  Ring or thin walled cylinder inertia(I) = MR2

80.  Disc or solid cylinder inertia = ½ MR2

81.  Disc inertia = ½ M (R22 + R12 )

82.  Solid sphere inertia = 2/5 MR2

83.  Solid rod or meter stick inertia = 1/12 Ml2

84.  Rectangular plate inertia = 1/12 M (a2+b2)

85.  Angular momentum = L = r x p = r mv = rmrω =r2mω = Iω

86.  L = rmv → L/t = rmv/t = rma = rF = τ

87.  L/t = τ

88.  Linear kinetic energy = ½ mv2

89.  Rotational kinetic energy = ½ Iω2

90.  Velocity of hoop = v =

91.  Velocity of disc = v =

92.  Critical velocity = v = 7.9 km2

93.  The orbital velocity = v =

94.  Lift at rest → T =w

95.  Lift moving downward → T = w – ma

96.  Lift moving upward → T = w + ma

97.  Lift falling freely = T  mg-ma = 0

98.  Frequency for artificial satellite → f =

Fluid dynamics

99.  Drag force → Fd = 6 πη r v

100.       Terminal velocity → vt =

101.       Continuity equation → A1 v1 = A2 v2

102.       Av=∆V/∆t = constant

103.       ∆m/∆t = ρ ∆V/∆t

104.       Bernoulli’s Equation = P + ½ ρv2 + ρgh = constant

105.       Torricelli’s Theorem → v =

106.       Flow meter or the venture meter → v1 =

Oscillation

107.       Frequency → f=1/T

108.       Angular frequency → ω = 2πf

109.       Time period → T = 2π/ω

110.       Velocity of projection → vy = ω

111.       Simple pendulum time period → T = 2π

112.       Simple pendulum potential energy = ½ kx2

113.       Simple pendulum kinetic energy = ½ kx02 -½ kx2

114.       Total energy of simple pendulum = ½ kx02

115.       Resonance frequency = Fn = nf1

116.       Phase → θ =ω t

Waves

117.       Transverse wave speed →

118.       Longitudinal waves speed →

119.       Phase change→ 2π = λ

120.       Phase difference → δ = 2π/λ

121.       Speed of sound by newton → v =  = 281 ms-1

122.       Laplace correction → v =  = 332 ms-1

Chap No.11   ELECTROSTATICS

123.       1 e = 1.602 x 10-19 C

124.       Q = ne

125.       Coulomb’s Law; F = k

126.       K =

127.       K = 9.0 x 109 N m2 C-2

128.       εo = 8.85 x 10 -12 C2 N-1 m-2

129.       εr =

130.       Fmed =

131.       E =  =  = K

132.       Ф = E A cos θ = N m2 C-1

133.       Ф =

134.       E due to sheet of charge;  E =

135.       E due to charge palates;     E =

136.       V =  =                             Volt = Joule / Coulomb

137.       Electric potential energy;  U =

138.       Electric potential;     V =   =  =

139.       Potential Gradient =  E = -

140.       1 eV =1.602 x 10-19 C x 1V           →   (1 eV = 1.602 x 10-19 J)

141.       C =  = C V-1 = farad

142.       Charge density;   σ =

143.       Cvac =  =  =

144.       εr = Cmed / Vvac

146.       Capacitors In Series;

147.       Q = Q1 = Q2 =Q3

148.       V =V1 + V2 + V3

149.       1/Ce = 1/C1 + 1/C2 + 1/C3

150.       Capacitors In Parallel;

151.       Q = Q1 = Q2 = Q3

152.       V = V1 + V2 +V3,

153.       Ce = C1 + C2 + C3

154.       Electric dipole; P = q d

155.       Energy = U =   =   (Ed)2

156.       Energy density; E2

157.       Maximum charge on capacitor = C x e.m.f

158.       q/q0 = 63.2 %          →for charging

159.       q/q0 = 36.7 %          →for discharging

160.       q = q0 (1-e-t/RC )       →for charging

161.       q = q0 e-t/RC               →for discharging

Chap No. 12   CURRENT ELECTRICITY

162.       Current, I = Q/t → C s-1 = A

163.       Drift velocity order = 10-5 m/s.

164.       V = IR

165.       Tan θ = I/V = 1/R

166.       Resistance, R = V/I  → 1Ω = 1V/1A

167.       R = ρ L/A  → Ω.m

168.       Conductance, G = 1/R  → Siemen(S)  or mho

169.       Conductivity, σ = 1/ρ =L/RA   →mho/m or S/m

170.       Pure metals R inc with T inc.

171.       Electrolytes and insulators, R dec with T inc.

172.       ΔR = αR0 T   → RT  = R0 (1+αT)

173.       Temperature co-efficient of Resistance, α =  RT  – R0/R0T   → K-1

174.       Resistivity, ρ T  = ρ 0 (1+αT)  OR   α =  ρ T  – ρ 0/ ρ 0T   → K-1

175.       Electromotive Force, ε = W/q     → 1 volt = 1 joule/coulomb

176.       Open circuit, I = 0 so  V= ε

177.       Terminal Voltage, Vt = ε - Ir

178.       Power,  P = W/t = VI    → 1 Watt = 1V x 1A

179.       1 kWh = 1 unit of electrical energy

180.       1 J = 1W x 1s

181.       Maximum output power,  (Pout)max = ε2 /4r = ε2 /4R

182.       Thermo emf,    ε = αT + ½ βT2

183.       KCL, ƩI = 0

184.       KVL,  Ʃε = ƩV = ƩIR

185.       KCL based on L.O.C.O.CHARGE

186.       KVL based on L.O.C.O.ENERGY

187.       Wheatstone Bridge,  X = PQ/R

188.       Potentiometer,  ε2 /ε1 = I2 /I1

189.       Tan θ = I/V = 1/R

Chap No. 13  ELECTROMAGNETISM

190.       Force on current carrying wire, F=BIL sin θ.

191.       Magnetic field or magnetic induction, B = F/IL →1 tesla =1 NA-1 m-1 = 1 Wb m-2

192.       1 T = 104 G

193.       Magnetic Flux,    Ф = B A cos θ     → 1 Wb = 1 N m A-1.

194.       Ampere’s Law,   B  I/r = μ0 (I/2πr)    OR      ƩB.ΔL = μ0 I

195.       Bnet = B1 + B2

196.       Magnetic field due to current carrying solenoid,  B = μ0 n I  → n=N/L

197.       Motion of charge particle in uniform magnetic field,    F=q v B sin θ

198.       Centripetal Force = Magnetic force   → mv2/r = qvB

199.       Time period of charge particle in B,        T = 2πm/qB

200.       Frequency of charge particle in B,       f = qB/2πm

201.       Velocity selector,              FE = FM  →   qE = qvB     → v = E/B

202.       Torque on current carrying coil,    τ = NBIA cos θ

203.       Ρestoring torque,      τ = C θ

204.       Galvanometer,   NBIA cos θ = C θ    → I = Cθ/NAB    → I  θ

205.       Conversion of galvanometer into ammeter,  small R connected in parallel

206.       Conversion of galvanometer into voltmeter,     large R in series are connected

207.       Ammeter,   Rs = Rg Ig / (I – Ig)      → Ideal ammeter → 0 R

208.       Voltmeter,   Rh = (V/Ig) – Rg                → Ideal voltmeter → infinite R

Chap No. 14 ELECTROMAGNETIC INDUCTION

209.       Faraday’s Law,   ε  N (ΔФ/Δt)    → ε = N (ΔФ/Δt )

210.       Lenz Law,     ε = –N (ΔФ/Δt )

211.       Flux motional emf,   ε = Blv sin θ

212.       Rate of work done,   W= Bilv

213.       Rate of production of electrical energy,    energy =ε I

214.       W = energy   → Bilv = εI  → ε = Blv

215.       Power,   P = F v

216.       ε = L ΔI/Δt   or ε = N ΔФ/Δt   → LI = NФ

217.       Self-Inductance,    L = NФ /I

218.       ε = M ΔI/Δt   or ε = N ΔФ/Δt   → MI = NФ

219.       Mutually inductance,   M = NФ /I

220.       F = 1/T

221.       Induced emf,  ε = NAB cosωt   or  NAB ω sinωt

222.       ε = εmax sin ωt

223.       Back emf,   V = ε + IR

224.       Ns / Np = Vs / Vp = Ip /Is

Chap 16    PHYSICS OF SOLIDS

225.       Elastic modulus =

226.       Tensile stress =

227.       Tensile strain =

228.       Young modulus =     = Nm-2

229.       Shear stress =

230.       Shear strain =   = tan θ

231.       Shear modulus = rigidity modulus =  =

232.       Bulk or volume stress =

233.       Bulk modulus (in fluids) = Δp =

234.       Volume strain =-

235.       Bulk modulus =  =

236.       Stress  strain (Hook’s law)

237.       A =  r2

238.       W = ½Fe   (work done on stretching wire).

239.       Strain energy = ½ F e

240.       Strain energy per unit volume =   = ½ (stress) (strain )

Chap 18    DAWN OF MODERN PHYSICS

241.       E = m0  c2

242.       L= L0

243.       T = t0

244.       M = m0

245.       λmax T = 0.2898 x 10-2 m k     (Wein’s displacement law)

246.       E = σ T4                                     (Steffan-Bolts Law)

247.       σ = 5.67 x 10-8 Wm-1 K-4

248.       E = n h f

249.       K.Emax = e V0

250.       K.Emax = h f – Ф

251.       H f0 = Ф =

252.       K.Emax = hf - Hf0

253.       Hf = K.E +hf’

254.       P=

255.       Δλ = 1-

256.        =  +  1-

257.       Ephoton = Eelectron + Epositron

258.       Photon rest mass energy = 2m0c2 = 1.02 MeV

259.        = mve-  + mve+

260.       λ =  =

261.       Δp =           and         Δx = λ

262.       (Δp)(Δx) = h

263.       (ΔE)(Δt) = h

Chap 19    ATOMIC SPECTRA

264.        = R (  -  )

265.       R =E0 / hc = 1.097 x 107m-1.

266.       mvr = nh/2π.

267.       h = planks constant = 6.6256 x 10-34 j s.

268.       E = hf = En – Ep

269.       rn =

270.       En = -

271.       En  = = 2.17 x 10-18 j/ n2 = +13.6 ev/ n2

272.       rn  = n2 r1 → r1 = 0.53 0A.

273.       1 0A = 10- m

274.       2πr=nλ

275.       eV → hfmax = hc/λmin

276.       λmin = hc/eV

277.       excited state for 10-8 s.

278.       metastable state for 10-3 s

Chap 20  NUCLEAR PHYSICS

279.       Nuclear size is of the order of 10-14 m.

280.       The mass of the nucleus is of the order of 10-27 kg.

281.       ½ mv2 = Vq

282.       Bqv = mv2/r

283.       Bqv = mv2/r → m = Bqr/v

284.       ½ mv2 = Vq → v2 = 2Vq/m

285.       So m = qr2B2/2V

286.   Δm = Zmp + Nmn – M(A,Z)

287.       The binding energy in MeV is 931 x Δm.

288.       The binding energy per nucleon = Eb/A.

289.       0n1 → 1H1 + -1β0 + antineutrino 12 MIN

290.       ΔN/Δt =-λN

291.       R =- ΔN/Δt =λN

292.       N= N0e-λt

293.       1 Bq = 1 decay per second

294.       1 Ci = 3.70 x 1010 decay/s

295.       λT ½ = 0.693

296.       The charge on u,t and c, in term of electron is +2/3e.

297.       The charge on s,t and b in term of electron is -1/3e.

298.       proton =2U→D.

299.        neutron

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