(A) The rotational kinetic energy is given by $K = \frac{L^2}{2I}$,where $L$ is the angular momentum and $I$ is the moment of inertia.Since there are

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(A) The rotational kinetic energy is given by $K = \frac{L^2}{2I}$,where $L$ is the angular momentum and $I$ is the moment of inertia.Since there are no external torques acting on the system,the angular momentum $L$ remains constant.Therefore,the kinetic energy is inversely proportional to the moment of inertia: $K \propto \frac{1}{I}$.Let $I_i$ and $K_i = E$ be the initial moment of inertia and initial kinetic energy,respectively.Let $I_f$ and $K_f$ be the final moment of inertia and final kinetic energy,respectively.Given that $I_f = 3I_i$,we have:$\frac{K_f}{K_i} = \frac{I_i}{I_f} = \frac{I_i}{3I_i} = \frac{1}{3}$.Thus,$K_f = \frac{K_i}{3} = \frac{E}{3}$.Comparing this with $\frac{E}{x}$,we get $x = 3$.

Class 11 Physics System of Particles and Rotational Motion Conservation of angular momentum (combined translation and rotational motion)

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$A$ circular plate is rotating in a horizontal plane about an axis passing through its center and perpendicular to the plate with an angular velocity $\omega$. $A$ person sits at the center holding two dumbbells. When he stretches out his hands,the moment of inertia of the system becomes triple. If $E$ is the initial kinetic energy of the system,then the final kinetic energy will be $\frac{E}{x}$. The value of $x$ is $....$

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$3$
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$6$
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$9$
D
$12$

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Class 11

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System of Particles and Rotational Motion

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Conservation of angular momentum (combined translation and rotational motion)

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State and explain the law of conservation of angular momentum.

Medium

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$A$ thin circular ring of mass $M$ and radius $R$ is rotating about its axis with a constant angular velocity $\omega$. Four objects,each of mass $m$,are kept gently on the opposite ends of two perpendicular diameters of the ring. The new angular velocity of the ring will be:

MediumAIPMT 2003

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$A$ thin uniform circular disc of mass $M$ and radius $R$ is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with an angular velocity $\omega$. Another disc of same dimension but of mass $M/4$ is placed gently on the first disc coaxially. The angular velocity of the system now is

MediumIIT 1986

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Two small beads are initially at $A$ on an equilateral triangle made of uniform wires. The triangle is rotated about the vertical axis $AO$. The beads are released from rest simultaneously and slide down along $AB$ and $AC$ respectively (as shown in the figure). Which quantities are conserved as the beads slide down? (Friction is negligible)

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$A$ uniform disc of mass $M$ is rotating with a constant angular velocity $\omega$ about an axis passing through its center and perpendicular to its plane. Let its angular momentum be $L$. $A$ drop of molten plastic falls onto the disc and sticks to it. Which of the following remains constant?

State and explain the law of conservation of angular momentum.

$A$ thin circular ring of mass $M$ and radius $R$ is rotating about its axis with a constant angular velocity $\omega$. Four objects,each of mass $m$,are kept gently on the opposite ends of two perpendicular diameters of the ring. The new angular velocity of the ring will be:

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