#Interconversion_of_formulas

1. Formulas related to 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 accelration

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

1. Formulas related to 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 accelration

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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