Lagrangian Dynamics - Problem 13 - Rolling motion on inclined plane

13 - Lagrangian Dynamics – Problem 13 – Rolling motion on inclined plane
In this video, we explore the fascinating physics of a rolling body on an inclined plane using Lagrangian mechanics. Step by step, we derive the equations of motion, apply the rolling constraint, and uncover how acceleration depends on the body’s moment of inertia.
🔹 Topics covered:
• Setting up generalized coordinates for rolling motion
• Translational and rotational kinetic energy
• Potential energy on an inclined plane
• Applying the rolling constraint i.e. rolling without slipping
• Deriving acceleration for cylinders, spheres, and hollow bodies
• General formula for rolling motion using Lagrangian mechanics
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🛠️ Prerequisites
Basic calculus (derivatives, chain rule)
High school physics (velocity, acceleration, energy)
No forces, no torques, no free-body diagrams needed!
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📚 Resources & Further Reading
Goldstein’s Classical Mechanics (Ch. 1–2)
Feynman Lectures, Vol. I, Ch. 19
Classical Mechanics by J C Upadhyaya
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