Consider a cone with half angle is placed such a way that vertex is at origin and its axis Is along z direction. Obtain the expression for radial acceleration of a particle of mass m is constrained to move on the surface of the cone by taking Lagrangian in terms of spherical polar coordinates rand (Assume is the angular momentum along z direction). 12 m²² sin² a gcosa 12 m²r³ sin² a -gcosa 12 mrsina 1 2 g cosa m²r sin a gcosa
Consider a cone with half angle is placed such a way that vertex is at origin and its axis Is along z direction. Obtain the expression for radial acceleration of a particle of mass m is constrained to move on the surface of the cone by taking Lagrangian in terms of spherical polar coordinates rand (Assume is the angular momentum along z direction). 12 m²² sin² a gcosa 12 m²r³ sin² a -gcosa 12 mrsina 1 2 g cosa m²r sin a gcosa
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Transcribed Image Text:Consider a cone with half angle is placed such a way that vertex is at origin and its axis Is along z direction. Obtain the expression for radial acceleration of a particle of mass m is constrained to move on the surface
of the cone by taking Lagrangian in terms of spherical polar coordinates rand (Assume is the angular momentum along z direction).
12
m²² sin² a
gcosa
12
m²r³ sin² a
-gcosa
12
mrsina
1
2
g cosa
m²r sin a
gcosa
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