🔥Applied Physics-1st || Units And Dimensions || One-Shot || By- Anurag Sir

Units and Dimensions—Applied Physics, Unit 1

Anurag Sir presents a one-shot overview of the first unit of Applied Physics. The lecture covers why measurement matters, physical quantities and units, systems of units, dimensions, dimensional homogeneity, applications of dimensional analysis, and its limitations.

1. Why Measurement Is Needed

Measurement is essential in everyday life, science, and engineering. It tells us how much of something is involved and allows people to communicate quantities consistently. In engineering, reliable measurements help to:

• Make components and structures to the required sizes.
• Avoid errors that could waste materials or cause a machine or structure to fail.
• Maintain quality control during construction and manufacturing.
• Support safety and reliability.

The lecture uses examples such as buying a specified amount of milk or oil, measuring a pipe to fit through a doorway, and designing a bridge to handle loads.

2. Physical Quantities and Their Types

A physical quantity is something that can be measured. Examples include length, mass, time, temperature, speed, velocity, force, acceleration, work, power, energy, and electric charge.

Physical quantities are divided into:

• Fundamental quantities: Independent basic quantities that do not need to be expressed in terms of other quantities. Examples include length, mass, and time.
• Derived quantities: Quantities defined using fundamental quantities. For example, force depends on mass and acceleration: (F = ma). Area, work, and speed are also derived quantities.

A quantity’s unit expresses how it is measured. Fundamental quantities have fundamental units, while derived quantities have derived units. For instance, area has the derived unit square metre, and force can be measured in newtons.

3. Systems of Units

The lecture reviews three systems:

• FPS: Foot, pound, second; described as the British system.
• CGS: Centimetre, gram, second.
• MKS: Metre, kilogram, second.

The SI system is described as the internationally used, expanded form of MKS. Its seven base quantities and units are:

• Length — metre
• Mass — kilogram
• Time — second
• Temperature — kelvin
• Electric current — ampere
• Amount of substance — mole
• Luminous intensity — candela

The lecture also discusses plane angle and solid angle, measured in radians and steradians, respectively. Since these are ratios of like lengths or areas, they are dimensionless, though the lecture refers to them using the traditional syllabus term “supplementary” quantities.

4. Dimensions and Dimensional Formulas

Dimensions describe a physical quantity in terms of fundamental quantities. The lecture uses (M), (L), and (T) for mass, length, and time, with “Malti Devi” as a mnemonic.

Common examples include:

• Speed or velocity: ([LT^{-1}])
• Acceleration: ([LT^{-2}])
• Force: ([MLT^{-2}])
• Work: ([ML^2T^{-2}])

The lecture’s method for finding a dimensional formula is:

1. Identify the physical quantity.
2. Write its defining formula.
3. Determine the units of the quantities in that formula.
4. Substitute their dimensions, using (M), (L), and (T).
5. Simplify the powers to obtain the dimensional formula.

For example, (F = ma). Mass has dimension (M), and acceleration has dimension (LT^{-2}), so force has dimension ([MLT^{-2}]).

5. Principle of Dimensional Homogeneity

The principle of homogeneity states that terms added or equated in a valid physical equation must have matching dimensions. The lecture illustrates this by noting that five metres can be added to five metres, but a length cannot be added to a mass.

For the equation (v = u + at):

• (u) and (v) are velocities, each with dimension ([LT^{-1}]).
• Acceleration multiplied by time has dimension ([LT^{-2}][T] = [LT^{-1}]).

Thus, the terms are dimensionally consistent. Dimensional checking can test whether an equation may be correct, but it does not prove that the equation is physically correct.

6. Applications of Dimensional Analysis

The lecture presents dimensional analysis as a way to:

• Find the dimensions of a quantity from its defining equation.
• Determine its unit in a particular system.
• Convert a quantity from one system of units to another.
• Check whether a physical equation is dimensionally consistent.
• Derive a possible relationship between quantities.

For unit conversion, the lecture gives a general procedure: identify the quantity’s dimensions, note the base-unit values in the original and target systems, and use the powers in the dimensional formula to convert its numerical value. It works through the example that one dyne equals (10^{-5}) newton and discusses conversion between erg and joule systems.

To derive a relationship:

1. Identify the quantity being calculated and the quantities on which it depends.
2. Assume a proportional relationship with unknown powers—for example, (Q \propto x^a y^b).
3. Substitute the dimensions of each quantity.
4. Equate the powers of (M), (L), and (T) on both sides.
5. Solve for the unknown powers.
6. Include a dimensionless constant if appropriate; dimensional analysis alone does not determine its numerical value.

The lecture illustrates this with a quantity depending on gravitational acceleration (g) and height (h), leading to a relationship proportional to (\sqrt{gh}). It notes that a numerical coefficient such as 2 must come from experiment or other physical reasoning. It also sets up a centripetal-force example involving mass, speed, and radius.

7. Limitations of Dimensional Analysis

The lecture emphasizes that dimensional analysis is useful but cannot do everything. In particular, it:

• Cannot determine numerical dimensionless constants such as 2 or (\pi).
• Cannot distinguish quantities with the same dimensions, such as distance and displacement, or speed and velocity.
• Cannot by itself give the direction or other vector information.
• Does not establish that a dimensionally consistent equation is physically correct.
• Cannot determine whether a relationship involves functions such as sine, cosine, logarithms, or exponentials; those functional forms require other information.
• Has difficulty deriving a relation when there are more independent quantities than the available fundamental dimensions can constrain, or when quantities with identical dimensions make the unknown powers indistinguishable.

Speakers and Sources Featured

• Anurag Sir — the main lecturer and source of the explanations.
• Students and viewers in the live class or chat — brief questions and responses are included, but most are unnamed or unclear in the auto-generated subtitles.
• Rahul Sir and other named students or viewers — several names are addressed or mentioned, but the subtitles do not reliably establish them as sustained speakers.