(D) According to the law of conservation of angular momentum,if the external torque acting on the system is zero,the angular momentum $L = I\omega$ re

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It will decrease to less than $\omega$.

(D) According to the law of conservation of angular momentum,if the external torque acting on the system is zero,the angular momentum $L = I\omega$ remains constant.When the ice melts,the water spreads out on the table.This increases the moment of inertia $(I)$ of the system because the mass is distributed further away from the axis of rotation.In the formula $L = I\omega$,if $L$ is constant and $I$ increases,the angular velocity $\omega$ must decrease.Therefore,the rotational speed of the system will decrease to less than $\omega$.

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

Easy

$A$ block of ice is placed at the center of a circular table. The table rotates with an angular velocity $\omega$ about a vertical axis passing through its center. If the ice melts without evaporation,what will happen to the rotational speed of the system?

A
It will become zero.
B
It will remain constant at $\omega$.
C
It will increase to more than $\omega$.
D
It will decrease to less than $\omega$.

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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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$A$ 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?

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If the mass of the Earth is kept constant and its radius is reduced to half, then the duration of the day will become ........ $hr$.

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$A$ thin uniform circular disc of mass $M$ and radius $R$ is rotating with angular velocity $\omega$ in a horizontal plane about an axis passing through its centre and perpendicular to its plane. Another disc of the same radius but of mass $\frac{M}{3}$ is placed gently on the first disc co-axially. The new angular velocity will be:

DifficultMHT CET 2024

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$A$ hot solid sphere is rotating about a diameter at an angular velocity $\omega_0$. If it cools so that its radius reduces to $\frac{1}{\eta}$ of its original value,its angular velocity becomes .............

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$A$ block of ice is placed at the center of a circular table. The table rotates with an angular velocity $\omega$ about a vertical axis passing through its center. If the ice melts without evaporation,what will happen to the rotational speed of the system?

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$A$ thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect,the angular speed of the disc

$A$ 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?

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