Dimensions are the physical nature of a quantity and are expressed as combinations of base quantities such as length, mass, and time. They give you an understanding of what a physical quantity is made of and how it can be related to other quantities. 

The base dimensions in physics are:

• Length [L]

• Mass [M]

• Time [T]

• Electric current [I]

• Thermodynamic temperature [Θ]

• Amount of substance [N]

• Luminous intensity [J]

These base dimensions are combined to describe all physical quantities. For example, speed, which is the distance traveled per unit of time, has the dimension of length divided by time, expressed as [L][T]^-1.

Dimensional analysis is a technique used to understand the relationships between different physical quantities. It helps you check the correctness of equations, convert units from one system to another, and even derive relationships between physical quantities.

Key Steps in Dimensional Analysis:

1. Identify the Dimensions: Determine the dimensions of all physical quantities involved.

2. Construct the Dimensional Formula: Express the given physical quantity in terms of base dimensions.

3. Check Consistency: Ensure both sides of an equation have the same dimensions.

Dimensional analysis is a powerful tool in physics and engineering. It allows you to:

• Verify Equations: Ensure that equations are dimensionally consistent.

• Convert Units: Easily switch between different units of measurement.

• Derive Formulas: Infer relationships between different physical quantities even if the exact details are unknown.

Understanding the dimensions of physical quantities and mastering dimensional analysis will equip you with a crucial skill set for tackling complex problems in physics and engineering. By breaking down physical quantities into their base dimensions and using dimensional analysis, you can simplify and solve many challenges you'll encounter in your studies and beyond.

Keep practicing with different examples, and soon, dimensional analysis will become second nature to you. Happy learning!