Central Force Motion-I | Classical Mechanics | JRF Express | CSIR NET | Lec-16 | IFAS

Central Force Motion-I | Classical Mechanics | JRF Express | CSIR NET | Lec-16 | IFAS explained with clear concepts and exam‑focused approach. Covers central force motion concepts, effective potential tricks, circular orbit conditions, Bertrand’s theorem, and two‑body reduction to one‑body using reduced mass – all with problem‑solving strategies for CSIR NET, GATE, JEST, and TIFR aspirants. 🔥Join India's Best Coaching for CSIR NET and GATE Exams: https://ifasonline.com/csir-net/physi... 📞 Need Guidance? Call/WhatsApp: 9172266888 ━━━━━━━━━━━━━━━━━━━━━━━━━ ⏳ Lecture Timeline: [00:00:00] – Introduction to Central Force Motion-I [00:11:22] – F3 Derivation: q, p Functions & Integration [00:16:37] – Important: F3 Expression – eᵠ⁻¹ tan p [00:19:22] – Central Force: Definition & Properties [00:22:00] – Concept: Force = f(r) r̂, Radial Direction [00:23:41] – Angular Momentum Conservation (τ=0) [00:33:00] – Torque & Angular Momentum Proof [00:36:00] – Motion Lies in a Plane (ℓ = const) [00:39:28] – Spherical Symmetry & Conservative Nature [00:42:21] – Effective Potential: U_eff = U + ℓ²/(2μr²) [00:48:18] – Two‑Body → One‑Body Reduction [00:50:01] – Reduced Mass: μ = m₁m₂/(m₁+m₂) [00:55:08] – Lagrangian in Polar Coordinates [00:57:02] – Euler–Lagrange for r: Radial Equation [01:01:30] – Important: Radial Force = –dU_eff/dr [01:04:16] – Centrifugal Term in U_eff [01:05:13] – Orbital Energy: E = ½μṙ² + U_eff [01:06:35] – Circular Orbit: Condition du/dr = 0 [01:08:35] – Stable vs Unstable Circular Orbits [01:14:49] – Radial Oscillations around Stable Orbit [01:22:53] – Question 1: Radius Ratio from ℓ Ratio (Harmonic) [01:24:49] – Question 2: Total Energy of Circular Orbit (Harmonic) – HW [01:28:26] – Complete Session (Central Force Motion-I ) ━━━━━━━━━━━━━━━━━━━━━━━━━ 📖 Topics Covered in This Lecture: • Central Force Definition & Properties • Conservation of Angular Momentum Tricks • Two‑Body Problem & Reduced Mass Concepts • Lagrangian in Polar Coordinates & Effective Potential • Circular Orbit Stability (Stable & Unstable) • Bertrand’s Theorem & PYQ Applications • Small Radial Oscillations & Frequency Formula • Kepler & Harmonic Oscillator Potential Problems ━━━━━━━━━━━━━━━━━━━━━━━━━ 📚 Lecture Summary: In this session, IFAS Expert Faculty focuses on central force motion in classical mechanics. Key concepts include deriving the effective potential, the condition for circular orbits, stability analysis via second derivative of effective potential, and Bertrand’s theorem for power‑law forces. The two‑body problem is reduced to a one‑body problem using reduced mass. Problem‑solving tricks and PYQ discussions on central force motion are provided, strengthening conceptual clarity and exam readiness. ━━━━━━━━━━━━━━━━━━━━━━━━━ 🎓 This lecture is highly beneficial for students preparing for: ✅ CSIR NET Physical Science ✅ GATE Physics ✅ JEST Physics ✅ TIFR Physics ✅ BARC / DRDO / ISRO Exams ✅ SET / PhD Entrance Exams ━━━━━━━━━━━━━━━━━━━━━━━━━ 🏆 Why IFAS is India’s No. 1 Choice for CSIR NET & GATE Physics? (Our Results Speak): ✅ CSIR NET Dec 2025: 4000+ Selections (AIR 3, 8, 9.....) ✅ CSIR NET June 2025: 4200+ Selections (AIR 1, 2, 6, 10...) ✅ CSIR NET Dec 2024: 4000+ Selections (AIR 5, 6, 7, 8, 9...) ✅ CSIR NET June 2024: 2000+ Selections (AIR 3, 10, 13...) ✅ CSIR NET Dec 2023: 1200+ Selections (AIR 2, 4, 5...) 📄 View IFAS Result Sheet: 👉 https://drive.google.com/file/d/1THh6... ━━━━━━━━━━━━━━━━━━━━━━━━━ 🔗 Important Links: 🌍 Visit our Website: https://ifasonline.com 📞 Contact for Queries: 9172266888 📘 Free Counselling: https://ifasonline.com/csir-net/physi... ━━━━━━━━━━━━━━━━━━━━━━━━━ 🔗 India's Best Online Classes and Books: 🔥CSIR NET Physical Science Live & Recorded Course: https://ifasonline.com/csir-net/physi... 🎯 GATE Physics Recorded Course: https://ifasonline.com/gate/physical-... 📘CSIR NET Physical Science Books: https://ifasonline.com/csir-net/physi... ━━━━━━━━━━━━━━━━━━━━━━━━━ 📲 Download IFAS App: Android: https://play.google.com/store/apps/de... IOS: https://apps.apple.com/us/app/ifas/id... ━━━━━━━━━━━━━━━━━━━━━━━━━ Stay Updated Via Other Social Media: ✔ Telegram: https://t.me/csir_net_gate_physics ✔ Instagram:   / csir_net_physical_science   #centralforcemotion #classicalmechanics #jrfexpress #csirnetlecture #csirnet #csirnetphysicalscience #gatephysics #csirnetphysics #csirnetjune2026 #csirnetlecture #ifasphysics