Suppose a solid sphere of radius R rolls down a hemisphere of radius 5 R. 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! 2 Start by showing that the Lagrangian is: L (r, 0, 6) = mr² + ½{mr²0² + {mR²¢² – mgrcos(0)
Suppose a solid sphere of radius R rolls down a hemisphere of radius 5 R. 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! 2 Start by showing that the Lagrangian is: L (r, 0, 6) = mr² + ½{mr²0² + {mR²¢² – mgrcos(0)
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Need help understanding where the term 1/5mR^2Φ^2 came from in the Lagrangian
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)
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Step 1
Lagrangian:
Lagrangian for the motion of a particle is defined by the equation,
where is the total kinetic energy of the particle and is the total potential energy of the particle.
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