Units And Measurements

Physical Quantity

A quantity that can be measured and expressed using a number + unit.

Example:

5 = numerical value
m = unit

SI Base Quantities

Quantity	SI Unit	Symbol
Length	metre	m
Mass	kilogram	kg
Time	second	s
Temperature	kelvin	K
Electric current	ampere	A
Amount of substance	mole	mol
Luminous intensity	candela	cd

Fundamental Dimensions

Mass:

[M]

Length:

[L]

Time:

[T]

Important Dimensional Formulae

Velocity:

[LT^−1]

Acceleration:

[LT^−2]

Force:

[MLT^−2]

Momentum:

[MLT^−1]

Work/Energy:

[ML^2T^−2]

Power:

[ML^2T^−3]

Pressure:

[ML^−1T^−2]

Density:

[ML^−3]

Frequency:

[T^−1]

Principle of Dimensional Homogeneity

Both sides of a physical equation must have the same dimensions.

Example:

s=ut+1/2*at

Dimensions:

L=L+L

Correct ✅

Uses:

Checking correctness of equations
Finding relations between quantities
Converting units

Types of Errors

Systematic Error

Error that occurs in a fixed pattern.

Example:
A weighing machine always shows +2 kg extra.

Random Error

Error that changes unpredictably.

Example:

5.1, 5.2, 5.0

Gross Error

Human mistakes.

Example:
Wrong reading, calculation mistake.

Accuracy and Precision

Accuracy

Closeness to the true value.

Precision

Closeness between repeated measurements.

Absolute Error

Difference between measured value and true/mean value.

Absolute error=∣Measured value−True value∣

Mean Absolute Error

For multiple readings:

Δa=∑∣errors∣/n

Relative/Fractional Error

Fractional error=Absolute error/Measured Value