When quantities are added or subtracted
Measurements & Uncertainties - OCR A-Level Physics
- When quantities are added or subtracted, add the absolute uncertainties.
- When quantities are multiplied or divided, add the percentage uncertainties.
- When a quantity is raised to a power n, multiply the percentage uncertainty by n.
$$\begin{aligned}
\text{If } y &= a \pm b: \quad \Delta y \\
&= \Delta a + \Delta b
\end{aligned}$$
$$\begin{aligned}
\text{If } y &= ab \text{ or } y \\
&= \frac{a}{b}: \quad \frac{\Delta y}{y} \\
&= \frac{\Delta a}{a} + \frac{\Delta b}{b}
\end{aligned}$$
$$\begin{aligned}
\text{If } y &= a^n: \quad \frac{\Delta y}{y} \\
&= n \times \frac{\Delta a}{a}
\end{aligned}$$
Examiner Tips and Tricks
- The powerThe rate of energy transfer. Measured in watts (W). rule is the one students forget most.
- If v appears as \(v^{2}\) in kinetic energyThe capacity to do work. Measured in joules (J).The energyThe capacity to do work. Measured in joules (J). an object possesses due to its motion. ($E_{k} = 1/2 mv^2)$, the percentage uncertainty in E_k from v is DOUBLE the percentage uncertainty in v.
- If you measure r for the volume of a sphere ($V = 4/3 \pi r^3)$, the percentage uncertainty in V is THREE times that in r.
Common Mistake
MEDIUM
Wrong: Adding percentage uncertainties when quantities are added or subtracted.
Right: For addition/subtraction of quantities, add ABSOLUTE uncertainties. For multiplication/division, add PERCENTAGE uncertainties. The rule depends on the mathematical operation, not the quantities.
Right: For addition/subtraction of quantities, add ABSOLUTE uncertainties. For multiplication/division, add PERCENTAGE uncertainties. The rule depends on the mathematical operation, not the quantities.