Solution Found!

Write down the Lagrangian for a cylinder (mass m, radius

Chapter 7, Problem 7.16

(choose chapter or problem)

Get Unlimited 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.

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.

                                   

 

Add to cart


Study Tools You Might Need

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back