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Statement of a problem № 3456

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A uniform spherical ball of mass m rolls without slipping down a wedge of mass M and angle d, which itself can slide without friction on a horizontal table. The system moves in the plane shown in Fig. 7.12. Here g denotes the gravitational acceleration. (a) Find the Lagrangian and the equations of motion for this system. (b) For the special case of M = m and d = pi/4 find (i) the acceleration of the wedge and (ii) the acceleration of the ball relative to the wedge. Useful information: Moment of inertia of a uniform sphere of mass m and radius R is I = 2/5mR^2

Solution:
A uniform spherical ball of mass m rolls without slipping down a wedge of mass M

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