1. Dimension of a Physical Quantity:
* Definition: The dimension of a physical quantity refers to the fundamental physical quantities it depends on. It tells us the *type* of quantity we're dealing with, not its specific numerical value.
* Example:
* Speed: Dimension is [L/T], meaning it depends on length (L) and time (T).
* Force: Dimension is [M L/T²], meaning it depends on mass (M), length (L), and time (T).
* Fundamental Dimensions: The basic building blocks of dimensions are called fundamental dimensions. Typically, they are:
* Length (L)
* Mass (M)
* Time (T)
* Electric current (I)
* Temperature (Θ)
* Amount of substance (N)
* Luminous intensity (J)
2. Dimensional Formula:
* Definition: The dimensional formula of a physical quantity expresses its dimensions using the fundamental dimensions and their powers.
* How it's written: We enclose the symbols of fundamental dimensions within square brackets and use exponents to indicate their powers.
* Example:
* Speed: Dimensional formula is [L¹T⁻¹]
* Force: Dimensional formula is [M¹L¹T⁻²]
Key Points to Remember:
* Dimensional analysis: We can use dimensional formulas to check the validity of physical equations. The dimensions on both sides of an equation must be the same.
* Unitless quantities: Some quantities like angles and refractive index have no dimensions (they're ratios of similar quantities).
* Dimensions vs. Units: Dimensions are fundamental concepts, while units are specific ways of measuring those dimensions. For example, speed's dimension is [L/T], but its unit could be meters per second (m/s), kilometers per hour (km/h), etc.
In a nutshell:
* Dimension: Tells us what kind of quantity we're dealing with (length, mass, time, etc.).
* Dimensional Formula: A mathematical expression using fundamental dimensions and their powers to represent the dimensions of a physical quantity.
