Question

Two unequal masses m and 3m are attached to a thin bar of negligible mass that rotates about an axis perpendicular to the bar. When m is a distance 3d from the axis and 3m is a distance d from the axis, the moment of inertia of this combination is i.

Answer 1

The moment of inertia of this combination is 7/3i

Solution:

Masses are m and 3m

The distance mass m = 3d

The distance mass 3m = d

we know

The Moment Inertia of the masses

I = m (3d)²+3m (d)²

I = 12md²

The Moment & Inertial of the masses

The distance mass m = d

The distance mass is 3m =  3d

I₁ = m(d)² + 3m (32)

I, = 28 d²m

I₁ = 7/31 i

Two unequal masses have the same momentum and the kinetic energy of the heavier mass becomes the kinetic energy of the lighter mass. If two unequal masses have the same kinetic energy, the heavier mass has more momentum. According to Newton's second law of motion, the acceleration of a body depends on both force and mass. So if the colliding objects have unequal masses, the contact forces created during the collision will result in unequal acceleration.

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