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**1. A weightless rod carries towards of masses M and M. The roads Hinge Joint to vertical axis OO
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^{'}, which rotates with an angular velocity ω. Determine the angle φ formed by the rod and there vertical.**
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The attempt at a solution

If I am not wrong, the two ways to ensure equilibrium are ensuring net force=0, or net torque=0.

i) Net force=0:

The center of mass of the system will be at a distance $$\frac{Ma}{m+M}$$ from mass m between M and m.

Therefore the F=ma eqn. perpendicular to the rod for the imaginary mass (m+M) seems to be

Now, the second ans, φ=0, is given in the book in the ans section, but the first ans is wrong.

If we start balancing the torque, then this eqn. comes again as the distance between the hing and the point of actions of the centrifugal forces are same.

Above is the answer given in the book.

The attempt at a solution

If I am not wrong, the two ways to ensure equilibrium are ensuring net force=0, or net torque=0.

i) Net force=0:

The center of mass of the system will be at a distance $$\frac{Ma}{m+M}$$ from mass m between M and m.

Therefore the F=ma eqn. perpendicular to the rod for the imaginary mass (m+M) seems to be

Now, the second ans, φ=0, is given in the book in the ans section, but the first ans is wrong.

If we start balancing the torque, then this eqn. comes again as the distance between the hing and the point of actions of the centrifugal forces are same.

Above is the answer given in the book.