Homogeneous equation
Physical Quantities & Units - OCR A-Level Physics
Key Definition
Homogeneous equation
An equation where every term has the same base units. The units on the left-hand side must equal the units on the right-hand side.
An equation where every term has the same base units. The units on the left-hand side must equal the units on the right-hand side.
- To check homogeneity, replace every quantity with its base units.
- Simplify the units on each side of the equation.
- If both sides have the same base units, the equation is homogeneousAn equation is homogeneous if all terms have the same SI base units. Used to check if equations are dimensionally consistent..
- Only quantities with the same units can be added or subtracted.
- Pure numbers and angles (radians) are dimensionless.
Common Mistake
MEDIUM
Wrong: Assuming a homogeneous equationAn equation where every term has the same base units. The units on the left-hand side must equal the units on the right-hand side. must be physically correct.
Right: Homogeneity only checks that units are consistent. It cannot detect missing dimensionless constants (like 1/2 in $E_{k} = 1/2 mv^2)$ or wrong signs. A homogeneous equationAn equation where every term has the same base units. The units on the left-hand side must equal the units on the right-hand side. may still be wrong.
Right: Homogeneity only checks that units are consistent. It cannot detect missing dimensionless constants (like 1/2 in $E_{k} = 1/2 mv^2)$ or wrong signs. A homogeneous equationAn equation where every term has the same base units. The units on the left-hand side must equal the units on the right-hand side. may still be wrong.
Examiner Tips and Tricks
- In a 'show that this equation is homogeneous' question, you MUST write the base units of every term separately, then show they match.
- Do not just say 'units are the same' without working.