Yoyo The figure below shows a crude model of a yoyo. A massless string4.suspended vertically from a fixed point and the other endaround a uniform cylinder of mass m and radius R. When the cylinder is released it.moves vertically down, rotating as the string unwinds. Write down the Lagrangian, usingthe distance x as your generalized coordinate. Find the Lagrange equation of motionand show that the cylinder accelerates downward with 2q/3.wrapped several times1Hints: You need to remember from your introductory physics course that the totalkinetic energy of a body like the yoyo is T = mu Iw, where v is the velocity ofthe center of mass, I is the moment of inertia (for a uniform cylinder, I =mR2) andw is the angular velocity about the CM. You can express w in terms of å.]xR

The total kinetic energy of the body is

Answered: Yoyo The figure below shows a crude…

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter7: Hamilton's Principle-lagrangian And Hamiltonian Dynamics

Section: Chapter Questions

Problem 7.1P

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