Units, dimensions and measurement

By the end of this lesson, you will be able to:

• Explain why units are fundamental in physics

• Distinguish between units and dimensions

• Use dimensional analysis to verify equations

• Apply significant figures correctly

• Quantify measurement uncertainty and error

1.1 The International System of Units

Physical Quantity | Symbol | SI Unit | Unit Symbol

Length L meter m

Mass m kilogram kg

Time s second s

Electric Current I ampere A

Temperature T Kelvin K

Amount of Substance n Mole Mol

Luminous Intensity Iv Candela cd

1.2 Derived units are formed by combining base units.

Examples:

Velocity ---> v = distance / time , v = m/s

Force ---> F = ma, Newton (N) = (kilogram . m / s^2)

2.Dimensions vs. Units

2.1 Dimensions

Fundamental dimensions

Length = L

Mass = M

Tİme = T

Examples:

Velocity = LT^(-1)

Acceleration = LT^(-2)

Force = MLT^(-2)

2.2 Units

A unit specifies how a dimension is measured.

Examples:

Units are meter, m/s, m/s^2 etc.

3.Dimensional Analysis

Dimensional analysis is a method used to verify the physical consistency of equations.

The dimensions of the left-hand side must match the dimensions of the right-hand side.

Consider the kinematic equation as shown ----> s=vt+1/2at^2

vt→(L/T)⋅T=L

at^2→(L/T^2)⋅T^2=L

3.1 Why Dimensional Analysis Is Useful?

• Detects incorrect formulas immediately

• Allows partial derivation of equations

• Helps eliminate incorrect answer choices

• Prevents unit-based calculation errors

4.Significant Figures