Applied Physics Units, Dimension and Measurements

This set covers vocabulary and fundamental concepts from the lecture on Units, Dimensions, and Measurements, including systems of units, dimensional analysis, measurement tools, error types, and significant figures.

Unit

The chosen standard of the same kind taken as reference in order to measure a physical quantity.

Physical quantities

All quantities in terms of which laws of physics can be expressed and which can be measured directly or indirectly.

Fundamental units

Units which can neither be derived from one another, nor can they be further resolved into any other units; there are seven fundamental and two supplementary units.

Derived units

The units of physical quantities which can be expressed in terms of a combination of two or more fundamental units.

System of units

A complete set of units, including both fundamental units and derived units.

CGS system

A system of units where the fundamental units of length, mass, and time are centimetre, gram, and second respectively.

FPS system

A system of units where the fundamental units of length, mass, and time are foot, pound, and second respectively.

MKS system

A system of units where the fundamental units of length, mass, and time are metre, Kilogram, and second respectively.

SI system

Abbreviation for Systeme Internationale d’ Units, a system introduced in 1960 by the General conference of weights and measures based on seven fundamental and two supplementary units.

Dimensions

The powers to which the fundamental units have to be raised in order to obtain the units of a physical quantity.

Principle of homogeneity

A principle stating that a physical relation must be dimensionally homogeneous, meaning the dimensions of all basic units must be individually and separately same in every term on both sides.

Dimensional formula: Density

$$[M L^{-3} T^0]$$

Dimensional formula: Velocity

$$[M^0 L T^{-1}]$$

Dimensional formula: Force

$$[M L T^{-2}]$$

Dimensional formula: Power

$$[M L^2 T^{-3}]$$

Vernier calipers

A measuring instrument used for measuring very short lengths and depths, such as the diameter of a small spherical body.

Vernier constant

The difference in the magnitude of one main scale division (M.S.D.) and one vernier scale division (V.S.D.); also known as the least count of the instrument.

Zero error

An error that occurs if the zeros of the main scale and the vernier scale (or circular scale) do not coincide when the jaws or studs are in contact.

Positive zero error

Occurs when the zero of the vernier scale is shifted to the right of the zero of the main scale, leadng to a reading higher than the actual value.

Negative zero error

Occurs when the zero of the vernier scale is shifted to the left of the zero of the main scale, leading to a reading lower than the actual value.

Screw Gauge

An instrument of higher precision than a Vernier Callipers, capable of measuring lengths accurately up to $0.01\,mm$ or $0.005\,mm$.

Pitch

The linear distance advanced by a screw in one complete rotation, usually equal to the separation between two consecutive threads.

Spherometer

A device used to measure the radius of curvature of a spherical surface, working on the principle of the micrometre screw.

Physical balance

A device that measures the gravitational mass of an object by comparing it with a standard mass, based on the principle of moments.

Systematic error

Errors which tend to be in one direction, either positive or negative, originating from instrumental flaws, technique imperfections, or personal factors.

Random errors

Errors that occur irregularly and are random in both sign and size; they can be minimized by taking the arithmetic mean of multiple observations.

Absolute error

The magnitude of the difference between the true (mean) value of a quantity and the individual measurement value.

Relative error

The ratio of the mean absolute error to the mean value of the quantity measured.

Percentage error

The relative error of a measurement expressed in percentage form.

Significant Figures

All digits in a result that are known reliably plus the first digit which is uncertain.