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Rigid Body Dynamics: Cylinder rolling over cart with spring

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Please see the attached file and solve number 7 only.

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Solution Summary

A two body system of cylinder rolling over a cart attached by spring. Velocity or cart and angular velocity of cylinder is determined.

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Please see the attached file.

Let the velocity of the cart when the spring is just reaches undeformed position is v and the velocity of the cylinder axis at this instant is vC,
As there is no external force acting on the system, applying the law of conservation of linear momentum we get
m*vC + M*v = ...

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