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Rotational Motion: Rod released on smooth horizontal plane

A thin rod of length h and mass M is held vertically with its lower end resting on a frictionless horizontal surface. The rod is then released to fall freely. Determine the speed of its center of mass just before it hits the horizontal surface. Use h, M, and g for length, mass, and gravitational acceleration respectively.

(b) What If? Now suppose the rod has a fixed pivot at its lower end. Determine the speed of the rod's center of mass just before it hits the surface. Use h, M, and g for length, mass, and gravitational acceleration respectively

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A thin rod of length h and mass M is held vertically with its lower end resting on a frictionless horizontal surface. The rod is then released to fall freely. Determine the speed of its center of mass just before it hits the horizontal surface. Use h, M, and g for length, mass, and gravitational acceleration respectively.
What If? Now suppose the rod has a fixed pivot at its lower end. Determine the speed of the rod's center of mass just before it hits the surface. Use h, M, and g for length, mass, and gravitational acceleration respectively.

Answer:
(a)

1) As there is no friction between the rod and the horizontal surface, there is no external force acting on the rod during the motion and the center of mass of the rod moves straight downwards.
2) As ...

Solution Summary

A rod is released from vertical position (a) on a smooth horizontal surface (b) about pivot at the lower end, and the velocity of the center of mass is calculated as the rod struck the horizontal surface.

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