The CSIR NET Physics examination, conducted by NTA, is scheduled for the last week of July 2025. With the date fast approaching, aspirants must now shift gears and focus on sections that offer both high weightage and conceptual depth. Among these, Classical Mechanics stands out—not only because it contributes around 8 to 10 questions in recent papers, but also because its topics are beautifully interconnected and predictable.

At Pravegaa, we’ve worked with thousands of students over the years, and we can tell you this: those who respect Classical Mechanics—not just memorize it—consistently perform well in the CSIR NET exam. Let me walk you through the themes you need to master and the mindset you should adopt.

1. Lagrangian Formalism: Where Mechanics Meets Symmetry

As you’ve likely noticed in your preparation, Lagrangian mechanics isn’t just about plugging into a formula—it’s about seeing the structure beneath the surface. The Euler-Lagrange equations allow us to describe motion elegantly, but their true power lies in how they reveal conserved quantities.

For instance, if a coordinate doesn’t appear explicitly in the Lagrangian, its associated momentum is conserved. This isn’t a coincidence—it’s a reflection of symmetry, and these symmetries are what the examiners love to test.

We often discuss these systems in class:

• The double pendulum and rotating pendulum—rich ground for applying conservation laws.
• Compound and spring pendulums—excellent for practicing coordinate choices.

If you’re still solving these problems mechanically, pause. Step back. Ask: What is the symmetry here? What should be conserved? That’s how you cross the threshold from rote learning to real insight.

2. Hamiltonian Formalism: A Bridge to Quantum Thinking

Students often treat Hamiltonian mechanics as just another conversion technique from Lagrangian mechanics. But as I remind my students, the Hamiltonian formalism is your entry point to understanding quantum mechanics.

In the exam, you’re likely to encounter:

• Conversion of Lagrangians to Hamiltonians via Legendre transformation.
• Time-dependent Hamiltonians and how they influence equations of motion.

Focus less on memorizing forms and more on grasping the structure. When you write down a Hamiltonian, ask yourself what it tells you about the energy landscape and how it evolves.

3. Poisson Brackets: Structure, Symmetry, and Scoring Opportunities

This is one of those topics where a well-prepared student can score full marks in seconds. But to reach that level, you must go beyond the definition.

Poisson Brackets reveal whether a quantity is conserved. They’re also used to verify if a transformation is canonical. Here’s what I ask my students to focus on:

• Practice calculating Poisson Brackets for simple and compound variables.
• Learn to use them as a diagnostic tool, not just an algebraic formality.

When used correctly, they become a powerful language—almost like commutators in quantum mechanics.

4. Generating Functions: The Canonical Toolkit

Whenever you see a problem on canonical transformations, think: Can I find the generating function? That’s the golden key.

Among the four types (F1 to F4), the paper often tests your ability to derive or identify the correct one. This isn’t just a symbolic game; it’s a conceptual skill. Learn to read a transformation and reverse-engineer its generator.

5. Newtonian Mechanics: Simplicity with Hidden Depth

Ironically, students often make mistakes in Newtonian mechanics because they assume it’s too easy. But NTA has a knack for twisting simple setups into subtle traps.

Pay special attention to:

• Free body diagrams in inertial frames (where Newton’s laws apply directly) and in non-inertial frames (where fictitious forces come into play), especially when dealing with multiple connected bodies.
• Friction problems in both one-dimensional and two-dimensional systems, particularly those involving angular motion or polar coordinates.

Your goal should be not just to solve, but to interpret the situation dynamically.

6. Small Oscillations: Where Linear Algebra Meets Physics

This topic demands a methodical, structured approach. If you’re not yet comfortable with the matrix method, now is the time.

Key areas include:

• Constructing kinetic and potential energy matrices.
• Solving the secular determinant for normal frequencies.

Students who approach this topic algebraically often get stuck. Those who treat it as a physical vibration problem with mathematical structure tend to excel.

7. Central Force Problems: Orbiting Toward Conceptual Mastery

Questions from this section are designed to test your intuition about motion under inverse-square laws.

Instead of memorizing formulas, focus on:

• Visualizing effective potential and understanding how it governs radial motion.
• Interpreting turning points and classifying orbits as bound or unbound.

Satellite motion and escape conditions frequently appear in CSIR papers-always tied to conservation principles.

8. Phase Space and Stability Analysis: Visual Thinking for Dynamic Systems

Students who can sketch and interpret phase curves have a serious advantage. This is where qualitative dynamics come into play.

Focus on:

• Identifying equilibrium points and classifying their stability.
• Using small oscillation analysis around those points to infer time periods.

We often work through phase portraits in our classes-not just for math, but to internalize system behavior.

9. Moment of Inertia: Tensor Thinking

While not always emphasized, this topic shows up when you least expect it. The inertia tensor, once understood, gives you full control over rigid body dynamics.

Practice computing the tensor for asymmetric bodies and determining angular momentum using it. Don’t just memorize formulas—see how symmetry simplifies computation.

10. Special Theory of Relativity: When Time and Space Interact

This is a favorite of NTA for conceptual questions. You’ll rarely need heavy math—but conceptual clarity is essential.

Be ready for:

• Lorentz transformation-based reasoning.
• Conservation of relativistic momentum and energy in collisions.
• Frequency shifts using the relativistic Doppler effect.

Approach this topic as a story of observers and frames. Once you adopt that mindset, the questions become intuitive.

In Closing

If you treat Classical Mechanics not as a syllabus block but as a language of physical reasoning, you’ll not only answer more questions-you’ll understand more physics. And that, as we emphasize at Pravegaa, is the ultimate goal.

The June 2025 CSIR NET Physics exam is a conceptual challenge, not a memory test. Prepare accordingly, and success will follow.

— Atul Gaurav
Co-founder, Pravegaa Education