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Question

Need help understanding where the term 1/5mR^2Φ^2 came from in the Lagrangian

Suppose a solid sphere of radius R rolls down a hemisphere of radius 5R. The coefficient of static friction is u. Will the sphere first start to slip, or will will it first leave the surface of the sphere? Hint: the problem now has TWO constraint equations! Start by showing that the Lagrangian is: L (r, 0, 6) = {{mr² + ½{mr²0² + {{mR² $² – mgrcos(0)
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Transcribed Image Text:Suppose a solid sphere of radius R rolls down a hemisphere of radius 5R. The coefficient of static friction is u. Will the sphere first start to slip, or will will it first leave the surface of the sphere? Hint: the problem now has TWO constraint equations! Start by showing that the Lagrangian is: L (r, 0, 6) = {{mr² + ½{mr²0² + {{mR² $² – mgrcos(0)
Expert Solution
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Step 1

Lagrangian: 

Lagrangian for the motion of a particle is defined by the equation,

L=K-U                                                                  (1)

where K is the total kinetic energy of the particle and U is the total potential energy of the particle.

 

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