1. A ball of mass m, radius r, and moment of inertia I = ?mr² rolls down a movable wedge of mass M. The angle of the wedge is 0, and it is free to slide on a frictionless horizontal surface. The ball rolls on the wedge without slipping. Let qı be the distance from the top of the wedge down the slope to the center of the ball, and let q2 be the horizontal position of the wedge. Find the Lagrangian for this system, and use it to find the acceleration of the wedge.
1. A ball of mass m, radius r, and moment of inertia I = ?mr² rolls down a movable wedge of mass M. The angle of the wedge is 0, and it is free to slide on a frictionless horizontal surface. The ball rolls on the wedge without slipping. Let qı be the distance from the top of the wedge down the slope to the center of the ball, and let q2 be the horizontal position of the wedge. Find the Lagrangian for this system, and use it to find the acceleration of the wedge.
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
Transcribed Image Text:mr? rolls down
a movable wedge of mass M. The angle of the wedge is 0, and it is free to
slide on a frictionless horizontal surface. The ball rolls on the wedge without
slipping. Let q1 be the distance from the top of the wedge down the slope
1. A ball of mass m, radius r, and moment of inertia I
to the center of the ball, and let q2 be the horizontal position of the wedge.
Find the Lagrangian for this system, and use it to find the acceleration of
the wedge.
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