Homogeneity of Equation

Introduction

• Homogeneity means the units on both sides are equal.
• If an equation is in physics, it must be homogeneous.

Example

• Example: Velocity = Distance / Time.
  • Here, the units on the right-hand side are equal to the units on the left-hand side.

Calculation

• If the units are not the same on both sides of an equation, then it is not a physics equation.

Solving Equations

Example of a Spherical Ball

• Force: [Units of kilogram, meter, second]
• Speed: Meter per second
• Radius: Meter
• Determination of Units:
  • Units of C = kg meter^{-1} second^{-1}

Pressure Difference Equation

• Volume/Time = πP R^4 / 8ηL,
• Determination of Units:
  • It is essential to check the base units and other elements.

Other Examples

• S = Ut + 1/2 At²
  • Displacement: Meter
  • Balance of Units: Meter = Meter + Meter

Energy Related Question

• Thermal Energy = kg, meter^2 / second^2
• Cross-Sectional Area: Meter^2
• Temperature Difference: Kelvin
• Final Units: C = kg meter second^{-3} Kelvin^{-1}

Conclusion

• All formulas and equations should be homogeneous.
• Pay special attention to maintaining the balance of units when there is addition and subtraction.