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Write down the Lagrangian for a cylinder (mass m, radius
Chapter 7, Problem 7.16(choose chapter or problem)
Write down the Lagrangian for a cylinder (mass m, radius R, and moment of inertia I) that rolls without slipping straight down an inclined plane which is at an angle a from the horizontal. Use as your generalized coordinate the cylinder's distance x measured down the plane from its starting point. Write down the Lagrange equation and solve it for the cylinder's acceleration x. Remember that T = 4mv2 + z L02, where v is the velocity of the center of mass and co is the angular velocity.
Questions & Answers
QUESTION:
Write down the Lagrangian for a cylinder (mass m, radius R, and moment of inertia I) that rolls without slipping straight down an inclined plane which is at an angle a from the horizontal. Use as your generalized coordinate the cylinder's distance x measured down the plane from its starting point. Write down the Lagrange equation and solve it for the cylinder's acceleration x. Remember that T = 4mv2 + z L02, where v is the velocity of the center of mass and co is the angular velocity.
ANSWER:Step 1 of 4
The following are given by the question:
The kinetic energy of the cylinder is equal to the sum of the linear and rotational kinetic energy of the cylinder.
Here, is the mass, is velocity is inertia and is the angular velocity.