# PHYSICS FORMULAS

### 1. FORCE

- F = ma
- F = kx
- F = m(vf² – vi²/2S)
- F = mv/t
- F = md/t²
- F = m(vf – vi) /t
- F = Area × density × velocity²
- F = 1/2 mv²/d
- F = 1/2 Pv/d
- F = Power/velocity
- Fc = mv²/r
- Fc = mrw²
- Fc/2 = mv²/2r
- Fc = 2K.E/r
- F = Area × Stress
- F = pir² × stress
- F = YA × Strain
- F = YAl/L
- F = pressure × area
- F = change in momentum × time interval
- F = – 2mVx × Vx/2l
- F2 = F1/A1 × A2
- F = qE
- F = kQ/r²
- F = ILB sintheta
- F = q (v × B)
- F = qE + q(v × B)

### 2. Formulas related to energy and work

- Fd = k.e
- mgh = 1/2 mv²
- E = 1/2 kx²
- E = Ve
- E = nhf
- E = nhc/lambda
- E = Pc
- K.e = hf – work function = hf – hf° = hf – hc/w° (here w° is cutt off wavelength)
- E = 1/2 Pv
- mv²/2r= Fc/2
- K.E/r = Fc/2
- K.E = Fc×r/2
- K.e = 1.5 KT
- E = VQ
- E = Power × time
- E = Fvt
- % loss in K.e = v1² – v2²/v1² × 100
- % loss in P.e = h1² – h²/h1² × 100
- Energy lost due to air friction(Fh) = 1/2mv² – mgh (when body is thrown upward)
- Energy lost due to air friction(FS) = mgh – 1/2mv² (when body is thrown downward)
- E = 1/2 CV² (capacitor)
- E = R × hc (R is Rydberg’ constant)
- J = m-¹ × Js ms-¹
- hf kalpha x rays = EL – Ek
- hf kbeta x rays = EM – Ek
- Binding energy = mass defect × c²
- W = Fd Costheta
- W = nmgh (when person is climbing stairs)
- W = n(m+m) gh (when person is climbing stairs with some load)
- W = 0mgh + 1mgh + 2mgh + 3mgh ……. (in case of stacking bricks. For ist brick h=0. For 2nd brick h=1. For 3rd brick h=2 and so on)
- W = Fd = PA × change in V
- W = Q – change in U
- Q = mc × change in T
- T/273.16 = Q/Q3 (Thermodynamic scale)
- W = I²Rt
- W = emf×charge
- W = VQ
- W = 1/2 lF
- W = YAl²/2L
- W = StressAl²/2Strain
- W = PressureAl²/2Strain
- W = Fl²/2Strain

### 3. Formulas related to Power

- P = Fv
- P = E/t
- P = n(mgh/t)
- P = Fd/t
- P = mv²/2t

### 4. Formulas related to distance, displacement, velocity and acceleration

- d = vt
- d = at²
- d = (vf + vi/2) ×t
- d = 5t² (for distance in ‘n’ seconds)
- d = 5(2tn – 1) (for distance in ‘nth’ second)
- d = 1/2 mv²/F
- d = vit + 5t²
- d = v × underroot 2H/g
- d = vt = x°wt = x°2pi/T × t = x°2pift
- x = x° Sin wt
- x = x° Sin (underroot k/m) t
- vf = vi + at
- 2as = vf² – vi²
- 2as = (vi + at)² – vi²
- 2as = vf² – (vf – at) ²
- v = underroot Vfx² + Vfy²
- v = Power/Force
- v = 2×K.E/momentum (k.e = 1/2 Pv)
- v² = 2×Power×time/mass (P = mv²/2t)
- v = underroot 2as
- v = underroot gr (speed at highest point in a verticle circle)
- v = underroot 5gr (speed at lowest point in a verticle circle)
- v² = 2FS/m
- v² = 2E/m
- v² = 2Ve/m
- v = eBr/m (velocity of particle under action of magnetic force along circular path)
- v² = Force/Area.Density
- v = w underroot x°² – x²
- v = underroot k/m × underroot x°² – x²
- v = x°w (at mean position where x=0)
- v = x° underoot k/m
- v = v° underroot 1 – x²/x°² (for determining ratio b/w inst. Velocity and maxi. Velocity)
- v= x°2pif = x°2pi/T
- a = x°w² = x°w.w = vw = v.2pif
- Common velocity = m1v1/m1+m2
- vi² = Rg/Sin2theta
- v = underoot Tension×length/mass
- V = 2pi ke²/nh (speed of e- in nth orbit)
- Vn = V/n
- v = nh/2pimr (lambda = 2pir and lambda=h/p)
- ma = kx
- a = kx/m (SHM)
- a = – gx/l (Simple pendulum)
- ac = v²/r

### 5. Formulas related to wavelength ‘w’

- w = v/f
- w = 1/wave number
- w1 = 2l (when pipe is opened at both ends)
- w1 = 4l (when pipe is opened at one end)
- Delta w = Us/f (doppler shift)
- Wavelength for obs. = w – delta w = v/f – Us/f
- w = hc/Ve
- w = hc/E
- w = h/mv
- w = h/P as P = underroot 2mE so
- w = h/underroot 2mE (de Broglie wavelength)
- w = underroot 150/V A° (short method for de Broglie wavelength. This formula is applicable only for e-)
- 1/w = RH (1/p²-1/n²)
- Wmaxi/Wmini = n²/n²-p² (for determining ratio b/w maxi. Wavelength to mini. Wavelength for series of atomic spectrum)
- w = 2pir/n (n is no. of loops in a circle)
- h/mv = 2pir

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