Number 12.27.12.28 Please help me on for a particle moving in a plane in a rotating coordinate

Number 12.27.12.28 Please help me

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on for a particle moving in a plane in a rotating coordinate system OX'Y'. 12.27. A particle of mass m is confined to move on the inside surface of a smooth cone of half-angle a The vertex is at the origin and the axis of the cone is vertical. What is the angular velocity wof the particle so that it can describe a horizontal circle at a height h above the vertex? 12.28. A hoop of mass m and radius r rolls without slipping down an inclined plane of mass M with an angle of inclination o. The plane slides without friction on the horizontal surface. Find and solve Lagrange's equations for the system. 12 29. Tn maspes on for a particle moving in a plane in a rotating coordinate system OX'Y'. 12.27. A particle of mass m is confined to move on the inside surface of a smooth cone of half-angle a The vertex is at the origin and the axis of the cone is vertical. What is the angular velocity wof the particle so that it can describe a horizontal circle at a height h above the vertex? 12.28. A hoop of mass m and radius r rolls without slipping down an inclined plane of mass M with an angle of inclination o. The plane slides without friction on the horizontal surface. Find and solve Lagrange's equations for the system. 12 29. Tn maspes