Physics · Mechanicsphy-1.1
Velocity
Length / Time or Displacement / Time taken
S.I. unit: m/s
Feature 01
Formula Bank
349 verified formulas, S.I. units and representations. Tip: switch to "Parameter" and type symbols like "v u a" to find equations that use them.
349 results
Physics · Mechanicsphy-1.2
Area
Length × Length
S.I. unit: m²
Physics · Mechanicsphy-1.3
Volume
Length × Breadth × Height
S.I. unit: m³
Physics · Mechanicsphy-1.4
Acceleration
Change in velocity / Time taken = (v - u) / t
S.I. unit: m/s²
Physics · Mechanicsphy-1.5
Force
Mass × Acceleration
S.I. unit: N or kg·m/s²
Physics · Mechanicsphy-1.6
Pressure
Force / Area (or P = ρRT/M)
S.I. unit: Pa or N/m²
Physics · Mechanicsphy-1.7
Energy
Force × Distance = Work done = F × d
S.I. unit: Joules (J)
Physics · Mechanicsphy-1.8
Power
Energy / Time taken = Work done / Time taken
S.I. unit: Watts (W)
Physics · Mechanicsphy-1.9
Density (ρ)
Mass / Volume
S.I. unit: kg/m³
Physics · Mechanicsphy-1.10
Equations Of Motion (1)
v = u + at
S.I. unit: m/s
Physics · Mechanicsphy-1.11
Equations Of Motion (2)
v² = u² + 2as
S.I. unit: (m/s)²
Physics · Mechanicsphy-1.12
Equations Of Motion (3)
s = ut + ½at²
S.I. unit: m
Physics · Mechanicsphy-1.13
Velocity under gravity
v = u ± gt
S.I. unit: m/s
Physics · Mechanicsphy-1.14
Displacement under gravity
s = ut ± ½gt²
S.I. unit: m
Physics · Mechanicsphy-1.15
Velocity–height relation (free fall)
v² = u² ± 2gh
S.I. unit: (m/s)²
Physics · Mechanicsphy-1.16
Time of flight (T)
T = 2u sinθ / g
S.I. unit: Seconds (s)
Physics · Mechanicsphy-1.17
Maximum height (H)
H = u² sin²θ / 2g
S.I. unit: Metres (m)
Physics · Mechanicsphy-1.18
Horizontal motion of a projectile
V_x = V₀ cosθ, Δx = (V₀ cosθ)t
S.I. unit: m/s
Physics · Mechanicsphy-1.19
Vertical motion of a projectile
V_y = V₀ sinθ, Δy = (V₀ sinθ)t + ½gt²
S.I. unit: m/s
Physics · Mechanicsphy-1.20
Momentum
Mass × Velocity
S.I. unit: kg·m/s
Physics · Mechanicsphy-1.21
Impulse
F × t = m(v - u)
S.I. unit: N·s
Physics · Mechanicsphy-1.22
Weight (W)
W = Mg
S.I. unit: N
Physics · Mechanicsphy-1.23
Resultant Force (F)
F - Mg = ma
S.I. unit: N
Physics · Mechanicsphy-1.24
Force due to varying mass
F = (Mass per second) × Velocity
S.I. unit: N
Physics · Mechanicsphy-1.25
Work (W)
W = F cosθ × L, FL, ΔP.E or ΔK.E
S.I. unit: Joules (J)
Physics · Mechanicsphy-1.26
Potential energy (U)
U = mgh
S.I. unit: Joules (J)
Physics · Mechanicsphy-1.27
Kinetic energy (K)
K = ½mv² (For Molecules = 3/2 kT)
S.I. unit: Joules (J)
Physics · Mechanicsphy-1.28
Total energy
E=U+K
S.I. unit: Joules (J)
Physics · Mechanicsphy-1.29
Angular velocity (ω)
ω = dθ/dt = 2π/T
S.I. unit: rad/s
Physics · Mechanicsphy-1.30
Linear velocity (v)
v = 2πr/T = ωr
S.I. unit: m/s
Physics · Mechanicsphy-1.31
Centripetal acceleration (a)
a = v²/r = ω²r
S.I. unit: m/s²
Physics · Mechanicsphy-1.32
Centripetal Force
F = mac = M(v²/r), F = mrω²
S.I. unit: N
Physics · Mechanicsphy-1.33
Maximum velocity on a curve
v = √(μrg) (μ = coefficient of friction)
S.I. unit: m/s
Physics · Mechanicsphy-1.34
Acceleration of Atwood machine
a = [(M₂ - M₁) / (M₁ + M₂)] g
S.I. unit: m/s²
Physics · Mechanicsphy-1.35
Tension in Atwood machine
T = [2M₁M₂ / (M₁ + M₂)] g
S.I. unit: N
Physics · Mechanicsphy-1.36
Acceleration (mass on smooth table)
a = [M₂ / (M₁ + M₂)] g
S.I. unit: m/s²
Physics · Mechanicsphy-1.37
Tension (mass on smooth table)
T = [M₁M₂ / (M₁ + M₂)] g
S.I. unit: N
Physics · Mechanicsphy-1.38
Acceleration (mass on inclined plane)
a = g [(M₂ - M₁ sinθ) / (M₁ + M₂)]
S.I. unit: m/s²
Physics · Mechanicsphy-1.39
Tension (mass on inclined plane)
T = [M₁M₂ g (1 + sinθ)] / (M₁ + M₂)
S.I. unit: N
Physics · Mechanicsphy-1.40
Escape Velocity (v_{esc})
v_{esc} = √(2GM / R_e) = √(2gR)
S.I. unit: m/s
Physics · Mechanicsphy-1.41
Total Orbital Energy (E)
E = K + U = -GMm / r
S.I. unit: Joules (J)
Physics · Mechanicsphy-1.42
Work done in gravitational field
W = GMm (1/r₁ - 1/r₂), W = m(v₁ - v₂)
S.I. unit: Joules (J)
Physics · Mechanicsphy-1.43
Time taken for a satellite
T² = 4π²r³ / (GM_e) = 4π²r³ / (g R_e²)
S.I. unit: Seconds (s)
Physics · Mechanicsphy-1.44
Moment (Torque)
τ = F × r (at an inclined angle θ = F × r sinθ)
S.I. unit: N·m
Physics · Mechanicsphy-1.45
Principle of moment
ACW moment = CW moment
S.I. unit: N·m
Physics · Mechanicsphy-1.46
Centripetal force
F = ma, a = v²/r, F = mv²/r
S.I. unit: N
Physics · Mechanicsphy-1.47
Acceleration of conical pendulum
a = (4π² l sinθ) / T²
S.I. unit: m/s²
Physics · Mechanicsphy-1.48
Period of a conical pendulum
T = 2π √(l cosθ / g)
S.I. unit: Seconds (s)
Physics · Mechanicsphy-1.49
Bulk Modulus (B)
B = -ΔP / (ΔV/V) = -V₀ ΔP / ΔV
S.I. unit: Pa or N/m²
Physics · Mechanicsphy-1.50
Shear modulus (G)
G = (F/A) / θ
S.I. unit: Pa or N/m²
Physics · Mechanicsphy-1.51
Gravitational potential energy
U = -G m₁ m₂ / r
S.I. unit: Joules (J)
Physics · Mechanicsphy-1.52
Total potential energy of three bodies
U_total = U₁₂ + U₁₃ + U₂₃
S.I. unit: Joules (J)
Physics · Mechanicsphy-1.54
Gravitational force (F_g)
F_g = (G M_1 M_2) / r²
S.I. unit: Newtons (N)
Physics · Mechanicsphy-1.55
Shear Stress (F/A)
F/A = G × Shear Strain (e)
S.I. unit: N/m²
Physics · Mechanicsphy-1.56
Shear Strain (θ)
θ = tan⁻¹(x/y)
S.I. unit: Dimensionless
Physics · Mechanicsphy-1.57
Compressibility (C)
C = 1/B = ΔV / (V_0 ΔP)
S.I. unit: m²/N
Physics · Mechanicsphy-1.58
Energy Per Volume
E/V = ½ × Stress × Strain
S.I. unit: J/m³
Physics · Mechanicsphy-1.61
Radius of gyration (k)
I = Mk² => k = √(I/M)
S.I. unit: Metres (m)
Physics · Mechanicsphy-1.62
Moment of inertia — rod (centre axis)
I = 1/12 ML²
S.I. unit: kg·m²
Physics · Mechanicsphy-1.63
Moment of inertia — rod (end axis)
I = 1/3 ML²
S.I. unit: kg·m²
Physics · Mechanicsphy-1.64
Rectangular plate (axis at
I = 1/12 M(a² + b²)
S.I. unit: kg·m²
Physics · Mechanicsphy-1.65
Rectangular plate (axis at
I = 1/3 Ma²
S.I. unit: kg·m²
Physics · Mechanicsphy-1.66
Moment of inertia — annular ring
I = 1/2 M(R_1² + R_2²)
S.I. unit: kg·m²
Physics · Mechanicsphy-1.67
Moment of inertia — solid disc
I = 1/2 MR²
S.I. unit: kg·m²
Physics · Mechanicsphy-1.68
Moment of inertia — hoop
I = MR²
S.I. unit: kg·m²
Physics · Mechanicsphy-1.69
Moment of inertia — solid sphere
I = 2/5 MR²
S.I. unit: kg·m²
Physics · Mechanicsphy-1.70
Kinetic energy of rotation
K.E = 1/2 Iω²
S.I. unit: Joules (J)
Physics · Mechanicsphy-1.71
Parallel axis theorem
I = I_cm + Md² (Parallel axis theorem)
S.I. unit: kg·m²
Physics · Mechanicsphy-1.72
Total kinetic energy of rolling body
K_Total = 1/2 I_cm ω² + 1/2 Mv_cm²
S.I. unit: Joules (J)
Physics · Mechanicsphy-1.73
Acceleration of rolling body on incline
a = (Mg sinθ) / (M + I/R²)
S.I. unit: m/s²
Physics · Mechanicsphy-1.75
Work done by Torque (W)
W = τ(θ_2 - θ_1) or ΔK.E_rotational
S.I. unit: Joules (J)
Physics · Mechanicsphy-1.76
Power
P = τω
S.I. unit: Watts (W)
Physics · Mechanicsphy-1.77
Angular momentum (L)
L = mvr sinθ or Iω or r × p
S.I. unit: kg·m²/s
Physics · Mechanicsphy-1.78
Pressure due to liquid column
P = ρhg
S.I. unit: Pa or N/m²
Physics · Mechanicsphy-1.79
Total pressure at depth
P = P_0 + ρhg
S.I. unit: Pa
Physics · Mechanicsphy-1.80
Buoyant force (F_b)
F_b = ρ_f V_f g
S.I. unit: Newtons (N)
Physics · Mechanicsphy-1.81
Net Upward force (F_net)
F_net = Vg(ρ_f - ρ_s)
S.I. unit: Newtons (N)
Physics · Mechanicsphy-1.82
Tension
T = Weight in air - Weight in fluid
S.I. unit: Newtons (N)
Physics · Mechanicsphy-1.83
Reynolds number (Re)
Re = ρvD / μ
S.I. unit: Dimensionless
Physics · Mechanicsphy-1.84
Continuity equation
A_1 V_1 = A_2 V_2
S.I. unit: m³/s
Physics · Mechanicsphy-1.85
Bernoulli's equation
P + 1/2 ρV² + ρhg = Constant
S.I. unit: J/m³ or Pa
Physics · Mechanicsphy-1.86
Flow rate (Q)
Q = AV = Volume / Time
S.I. unit: m³/s
Physics · Mechanicsphy-1.87
Capillary rise
H = (2γ cosθ) / (ρgr)
S.I. unit: Metres (m)
Physics · Mechanicsphy-1.88
Relative density (R.D)
Density of substance / Density of water
S.I. unit: Dimensionless
Physics · Mechanicsphy-1.90
Terminal velocity (V_t)
V_t = 2gr²(ρ_s - ρ_f) / (9η)
S.I. unit: m/s
Physics · Mechanicsphy-1.92
Co-efficient of viscosity (η)
η = 2gr²(ρ_s - ρ_f) / (9v)
S.I. unit: N·s/m² or Pa·s
Physics · Heat & Thermodynamicsphy-2.1
Average Speed
v_av = Total distance / Total time taken
S.I. unit: m/s
Physics · Heat & Thermodynamicsphy-2.2
Boyle's Law
P₁V₁ = P₂V₂
S.I. unit: Pa, atm
Physics · Heat & Thermodynamicsphy-2.3
Charles's Law
V₁/T₁ = V₂/T₂
S.I. unit: K⁻¹ or m³/K
Physics · Heat & Thermodynamicsphy-2.4
Pressure law
P₁/T₁ = P₂/T₂
S.I. unit: Pa/K
Physics · Heat & Thermodynamicsphy-2.5
Ideal gas law
PV = RT
S.I. unit: Pa·m³
Physics · Heat & Thermodynamicsphy-2.6
Fahrenheit to Celsius conversion
C = 5/9(F - 32)
S.I. unit: °C
Physics · Heat & Thermodynamicsphy-2.7
Celsius to Kelvin (Conversion)
K = 273 + C
S.I. unit: K
Physics · Heat & Thermodynamicsphy-2.8
Resistance thermometer temperature
θ°C = [(R_θ - R_0) / (R_100 - R_0)] × 100
S.I. unit: °C
Physics · Heat & Thermodynamicsphy-2.10
Linear expansivity (α)
α = ΔL / (L_0 ΔT)
S.I. unit: K⁻¹ or °C⁻¹
Physics · Heat & Thermodynamicsphy-2.11
Linear expansion
L₁ = L_0[1 + αΔT]
S.I. unit: m
Physics · Heat & Thermodynamicsphy-2.12
Area expansivity (β)
β = (A₁ - A₀) / (A₀ ΔT), β = 2α
S.I. unit: K⁻¹ or °C⁻¹
Physics · Heat & Thermodynamicsphy-2.13
Area of a solid after expansion
A₁ = A₀[1 + βΔT]
S.I. unit: m²
Physics · Heat & Thermodynamicsphy-2.14
Volume expansivity (γ)
γ = (V₁ - V₀) / (V₀ ΔT), γ = 3α
S.I. unit: K⁻¹ or °C⁻¹
Physics · Heat & Thermodynamicsphy-2.15
Volume expansion
V₁ = V₀[1 + γΔT]
S.I. unit: m³
Physics · Heat & Thermodynamicsphy-2.16
Heat Capacity (C)
C = Mass × c (where c is specific heat capacity)
S.I. unit: J/K
Physics · Heat & Thermodynamicsphy-2.17
Specific heat capacity (c)
c = Q / (mΔθ)
S.I. unit: J/kg·K or J/kg·°C
Physics · Heat & Thermodynamicsphy-2.22
Rate of heat conduction (thermal resistance)
ΔQ/Δt = (A ΔT) / R, where R = L / k_T
S.I. unit: m²·K / W
Physics · Heat & Thermodynamicsphy-2.24
Molecular Speed (V_rms)
V_rms = √(3RT / M)
S.I. unit: m/s
Physics · Heat & Thermodynamicsphy-2.26
Molar heat capacity
C = Q / (nΔT)
S.I. unit: J/mol·K
Physics · Heat & Thermodynamicsphy-2.27
Internal energy of a gas (ΔU)
ΔU = n C_v dT
S.I. unit: Joules (J)
Physics · Heat & Thermodynamicsphy-2.28
Work done at constant pressure
W = P(V_2 - V_1)
S.I. unit: Joules (J)
Physics · Heat & Thermodynamicsphy-2.29
Work done in isothermal expansion
W = nRT ln(V_2/V_1)
S.I. unit: Joules (J)
Physics · Heat & Thermodynamicsphy-2.30
Change in Kinetic energy (ΔK)
ΔK = n C_v (T_2 - T_1)
S.I. unit: Joules (J)
Physics · Heat & Thermodynamicsphy-2.32
Work done by a gas
W = Q - ΔU (where ΔU = Internal energy)
S.I. unit: Joules (J)
Physics · Heat & Thermodynamicsphy-2.33
Adiabatic relation
P₁V₁^γ = P₂V₂^γ
S.I. unit: Pa
Physics · Waves, Oscillations & Soundphy-3.2
Intensity (Sound) (I)
I=P/A
S.I. unit: W/m²
Physics · Waves, Oscillations & Soundphy-3.3
Acoustic Inverse Square Law
I₁ / I₂ = r₂² / r₁²
S.I. unit: Dimensionless
Physics · Waves, Oscillations & Soundphy-3.4
Beat Frequency (F_beat)
F_beat = f_a - f_b
S.I. unit: Hertz (Hz)
Physics · Waves, Oscillations & Soundphy-3.5
Time for beats
T_beat = (T_a T_b) / (T_b - T_a)
S.I. unit: Seconds (s)
Physics · Waves, Oscillations & Soundphy-3.6
Linear density (μ)
μ = m / l = ρ A r²
S.I. unit: kg/m
Physics · Waves, Oscillations & Soundphy-3.7
Opened pipe harmonics
f = (n+1)f_0
S.I. unit: Hertz (Hz)
Physics · Waves, Oscillations & Soundphy-3.8
Closed pipe harmonics
f = (2n+1)f_0
S.I. unit: Hertz (Hz)
Physics · Waves, Oscillations & Soundphy-3.9
Wave length of a closed pipe
λ = 4L
S.I. unit: Metres (m)
Physics · Waves, Oscillations & Soundphy-3.10
Wave length of an opened pipe
λ = 2L
S.I. unit: Metres (m)
Physics · Waves, Oscillations & Soundphy-3.11
Wave speed on a stretched string
V = √(T / μ)
S.I. unit: m/s
Physics · Waves, Oscillations & Soundphy-3.12
Wave speed in a solid rod
V = √(E / ρ)
S.I. unit: m/s
Physics · Waves, Oscillations & Soundphy-3.13
Wave speed in a fluid
V = √(B / ρ)
S.I. unit: m/s
Physics · Waves, Oscillations & Soundphy-3.15
Velocity of sound in a gas
V = √(γRT / M)
S.I. unit: m/s
Physics · Waves, Oscillations & Soundphy-3.16
Fundamental frequency of a string
f_0 = (1 / 2l) √(T / μ)
S.I. unit: Hertz (Hz)
Physics · Waves, Oscillations & Soundphy-3.17
Energy of stretched string
E = ½ L λ e² (or ½ Fe or ½ ke²)
S.I. unit: Joules (J)
Physics · Opticsphy-4.2
Refractive index of prism (minimum deviation)
n = sin((A+D)/2) / sin(A/2)
S.I. unit: Dimensionless
Physics · Opticsphy-4.3
Lens formula
1/f = 1/u + 1/v (Concave: 1/f = 1/u - 1/v)
S.I. unit: m⁻¹
Physics · Opticsphy-4.4
Number of images from inclined mirrors
n = 360/θ - 1 (θ = Angle of inclination)
S.I. unit: Dimensionless
Physics · Opticsphy-4.5
Angle of reflected ray
= 2θ (where θ = Angle of rotation)
S.I. unit: Degrees (°)
Physics · Opticsphy-4.7
Focal length (f)
f = r/2 (r = radius of curvature)
S.I. unit: cm or m
Physics · Opticsphy-4.8
Magnification (M)
M = v/u = h_i/h_o
S.I. unit: Dimensionless
Physics · Opticsphy-4.9
Power of lens (D)
P = 1 / (f in metres)
S.I. unit: Dioptres
Physics · Opticsphy-4.10
Optical Magnification (M)
M = θ'/θ = (h'/f)/(h/N) = N/f = 1 + N/f
S.I. unit: Dimensionless
Physics · Opticsphy-4.11
Magnification of telescope
M = f_o / f_e
S.I. unit: Dimensionless
Physics · Opticsphy-4.12
Magnification of compound microscope
M = (v_o/u_o) × (1 + D/f_e)
S.I. unit: Dimensionless
Physics · Opticsphy-4.13
Lens makers equation
1/f = (n - 1)[1/R_1 + 1/R_2]
S.I. unit: m⁻¹
Physics · Opticsphy-4.14
Path difference (Δ)
Δ = d sinθ (d = width of the aperture)
S.I. unit: Metres (m)
Physics · Opticsphy-4.15
Fringe position (Young’s double slit)
y_m = mλL / d
S.I. unit: Metres (m)
Physics · Opticsphy-4.16
Width of slit (d)
d = mλL / y_m
S.I. unit: Metres (m)
Physics · Opticsphy-4.17
Minimum angle of suspension
sinθ = 1.22 λ / d
S.I. unit: Degrees (°)
Physics · Opticsphy-4.18
Brewster angle (θ_B)
tanθ_B = n_2 / n_1
S.I. unit: Degrees (°)
Physics · Electricity & Magnetismphy-5.1
Capacitance of isolated sphere
C = 4πε₀R
S.I. unit: Farads (F)
Physics · Electricity & Magnetismphy-5.2
Capacitance of parallel plates
C = (ε₀A) / d
S.I. unit: Farads (F)
Physics · Electricity & Magnetismphy-5.3
Capacitance of cylindrical capacitor
C = (2πε₀L) / ln(b/a)
S.I. unit: Farads (F)
Physics · Electricity & Magnetismphy-5.4
Capacitance of spherical capacitor
C = (4πε₀ab) / (b - a)
S.I. unit: Farads (F)
Physics · Electricity & Magnetismphy-5.5
Capacitors in series
1/C_eq = 1/C₁ + 1/C₂ + 1/C₃ ... + 1/C_n
S.I. unit: Farads (F)
Physics · Electricity & Magnetismphy-5.6
Capacitors in parallel
C_eq = C₁ + C₂ + C₃ ... + C_n
S.I. unit: Farads (F)
Physics · Electricity & Magnetismphy-5.7
Energy stored in a capacitor
E = ½QV = ½CV² = Q² / 2C
S.I. unit: Joules (J)
Physics · Electricity & Magnetismphy-5.8
Energy density (u_E)
u_E = ½ε₀E²
S.I. unit: J/m³
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