(C) The angular velocity $\omega$ is given by $\omega = \frac{2\pi}{T}$.Given $T = 1 \ s$,we have $\omega = 2\pi \ rad/s$.The rotational kinetic energ

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Half the rotational kinetic energy

(C) The angular velocity $\omega$ is given by $\omega = \frac{2\pi}{T}$.Given $T = 1 \ s$,we have $\omega = 2\pi \ rad/s$.The rotational kinetic energy is $E_R = \frac{1}{2} I \omega^2$.Substituting the value of $\omega$: $E_R = \frac{1}{2} I (2\pi)^2 = \frac{1}{2} I (4\pi^2) = 2\pi^2 I$.Therefore,the moment of inertia $I = \frac{E_R}{2\pi^2}$.

Class 11 Physics System of Particles and Rotational Motion Rotational Kinetic Energy

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$A$ body completes one rotation in $1 \ s$. What is its moment of inertia if its rotational kinetic energy is $E_R$?

A
Equal to rotational kinetic energy
B
Twice the rotational kinetic energy
C
Half the rotational kinetic energy
D
Four times the rotational kinetic energy

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System of Particles and Rotational Motion

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Rotational Kinetic Energy

Two bodies $A$ and $B$ have moments of inertia $I_A$ and $I_B$, and angular momenta $L_A$ and $L_B$ respectively. Both of them have the same kinetic energy of rotation. The ratio of $L_A$ to $L_B$ is:

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An energy of $484\,J$ is spent in increasing the speed of a flywheel from $60\,rpm$ to $360\,rpm$. The moment of inertia of the flywheel is $.............\,kg\cdot m^2$.

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$A$ spherical solid ball of $1\,kg$ mass and radius $30\,cm$ is rotating about an axis passing through its centre with an angular velocity of $50\,rad/s$. The kinetic energy of rotation is ......... $J$.

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The rotational kinetic energy and translational kinetic energy of a rolling body are the same. The body is:

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Two rotating bodies $P$ and $Q$ of masses $m$ with moment of inertia $I_P$ and $I_Q$ $(I_Q > I_P)$ have equal kinetic energy of rotation. If $L_P$ and $L_Q$ are their angular momenta respectively,then:

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$A$ body completes one rotation in $1 \ s$. What is its moment of inertia if its rotational kinetic energy is $E_R$?

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Two bodies $A$ and $B$ have moments of inertia $I_A$ and $I_B$, and angular momenta $L_A$ and $L_B$ respectively. Both of them have the same kinetic energy of rotation. The ratio of $L_A$ to $L_B$ is:

An energy of $484\,J$ is spent in increasing the speed of a flywheel from $60\,rpm$ to $360\,rpm$. The moment of inertia of the flywheel is $.............\,kg\cdot m^2$.

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