A uniform disc, rotating freely about a perpendicular axis passing through its centre, makes n1 revolution per second. A small mass m falls vertically and sticks at a distance x from the axis of rotation. If rotational speed of the disc becomes n2 revolution per second, the moment of inertia of the disc is

Engineering

Physics

Conservation of Angular Momentum

Question

A uniform disc, rotating freely about a perpendicular axis passing through its centre, makes n₁ revolution per second. A small mass m falls vertically and sticks at a distance x from the axis of rotation. If rotational speed of the disc becomes n₂ revolution per second, the moment of inertia of the disc is

$\frac{n_{2} {mx}^{2}}{n_{1} + n_{2}}$

$\frac{n_{2} {mx}^{2}}{n_{1} - n_{2}}$

$\frac{n_{1} {mx}^{2}}{n_{1} - n_{2}}$

$\frac{n_{1} {mx}^{2}}{n_{1} + n_{2}}$

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In₁ = (I + mx²)n_L
I(n₁ – n₂) = mx²n₂
I = $\frac{{mx}^{2} n_{2}}{n_{1} - n_{2}}$

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