A horizontal rod AB which is held by frictionless bearings at its ends, can rotate freely around its horizontal axis. Two equal masses held in position, as shown, by rigid rods of negligible mass are symmetrically located relative to the centre of rod. If the system is rotating with angular velocity ω in absence of gravity, then choose the correct alternative(s).

Engineering

Physics

Conservation of Angular Momentum

Question

The reaction force at bearings on rod is downwards at A & upwards at B.

The angular momentum of system about point O is along axis of rotation.

There would be no reaction forces at bearings.

The reaction force at bearings on rod is upwards at A & downwards at B.

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$\vec{L}$ = $\vec{r} \times \vec{p}$
$\vec{L}$ = – $\frac{b}{2}$ 2° × m₂ ωa $\hat{k}$
= mωa $\frac{b}{2} (i \times \hat{k})$
$\vec{L}$ = mωa $\frac{b}{a} (\hat{y})$

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