SI Units Used In Classical Mechanics

Classical Mechanics is a field of physics that is used for studying the motion of objects. For example – Observing and understanding the motion of a ball thrown in the air comes under field of Classical Mechanics. As studying motion of objects involves a number of physical quantities like mass, velocity etc. that’s why Système International d’Unités(French Words) in short SI have defined certain rules about measurement of these quantities, which are globally accepted and are used across all the countries.

In this article, I have put together all of SI Units which are used in Classical Mechanics as a table, I hope this article help you.

Physical QuantityPhysical Quantity SymbolMathematical FormulaSI Unit of Physical Quantity
Reduced Massμμ = m1m2 / (m1 + m2)kg
Densityρρ = m/Vkg m-3
Relative Densitydd = ρ/ρ01
Surface DensityρA, ρSρA = m/Akg m-2
Specific Volumeυυ = V/m = 1/ρm3 kg-1
Momentumpp = mvkg ms-1
Angular MomentumLL = r x pJ s
Moment of intertiaII=\sum_{i} m_{i} r_{i}^{2}kg m2
ForceFF = dp/dt = maN
Moment of Force or TorqueM or TM = r x FN m
Potential EnergyEp , V, ΦE_{\mathrm{p}}=-\int \boldsymbol{F} \cdot \mathrm{d} \boldsymbol{r}J
Kinetic EnergyEk, T, KE_{\mathrm{k}}=(1 / 2) m v^{2}J
WorkW, A, wW=\int \boldsymbol{F} \cdot \mathrm{d} \boldsymbol{r}J
PowerPP = F.v = dW/dtW
Lagrange FunctionLL(q, \dot{q})=T(q, \dot{q})-V(q)J
Hamilton FunctionHH(q, p)=\sum_{i} p_{i} \dot{q}_{i}-L(q, \dot{q})J
ActionSS=\int L \mathrm{~d} tJ s
Pressurep, Pp = F/APa, N m-2
Surface Tensionσ\gamma=\mathrm{d} W / \mathrm{d} AN m-1, J m-2
WeightGG = mgN
Gravitational ConstantGF = Gm1m2/r2N m2 kg-2
Normal Stressσσ = F/APa
Shear Stressττ = F/APa
Linear Strainε\varepsilon=\Delta l / l1
Modulus of elasticity or Young’s ModulusEE = σ/εPa
Shear Strainγ\gamma=\Delta x / d1
Shear Modulus or Coulomb’s ModulusGG = τ/γPa
Volume or Bulk Strain\vartheta\vartheta=\Delta V / V_{0}1
Bulk or Compression ModulusKK=-V_{0}(\mathrm{~d} p / \mathrm{d} V)Pa
Dynamic Viscosityη\tau_{x z}=\eta\left(\mathrm{d} v_{x} / \mathrm{d} z\right)Pa s
Fluidity\varphi\varphi=1 / \etam kg-1 s
Kinematic Viscosity\nu\nu=\eta / \rhom2 s-1
Sound Energy FluxP, PaP = dE/dtW

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