(A) The rotational kinetic energy $(K_{rot})$ of the rotating body is given by $K_{rot} = \frac{1}{2} I \omega^2$. Given $I = 3 \ kg \cdot m^2$ and $\

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(A) The rotational kinetic energy $(K_{rot})$ of the rotating body is given by $K_{rot} = \frac{1}{2} I \omega^2$. Given $I = 3 \ kg \cdot m^2$ and $\omega = 3 \ rad/s$,we have: $K_{rot} = \frac{1}{2} \times 3 \times (3)^2 = \frac{1}{2} \times 3 \times 9 = 13.5 \ J$. The translational kinetic energy $(K_{trans})$ of the second body is given by $K_{trans} = \frac{1}{2} m v^2$. Given $m = 27 \ kg$ and $K_{trans} = K_{rot} = 13.5 \ J$,we have: $\frac{1}{2} \times 27 \times v^2 = 13.5$. $v^2 = \frac{13.5 \times 2}{27} = \frac{27}{27} = 1$. Therefore,$v = 1 \ m/s$.

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

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$A$ body rotating with an angular velocity of $3 \ rad/s$ has a moment of inertia of $3 \ kg \cdot m^2$ about its axis of rotation. The rotational kinetic energy of this body is equal to the translational kinetic energy of another body of mass $27 \ kg$. The speed of the $27 \ kg$ mass body is .......... $m/s$.

A
$1.0$
B
$0.5$
C
$1.5$
D
$2.0$

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System of Particles and Rotational Motion

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Rotational Kinetic Energy

$A$ ring of radius $0.5\, m$ and mass $10 \,kg$ is rotating about its diameter with an angular velocity of $20 \,rad/s.$ Its kinetic energy is .......... $J$.

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Two metallic spheres of equal outer radii are found to have the same moment of inertia about their respective diameters. Which of the following statement$(s)$ is/are true?

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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:

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$A$ body having a moment of inertia about its axis of rotation equal to $3 \ kg \ m^{2}$ is rotating with an angular velocity of $3 \ rad \ s^{-1}$. The kinetic energy of this rotating body is the same as that of a body of mass $27 \ kg$ moving with velocity $v$. The value of $v$ is: (in $m \ s^{-1}$)

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$A$ ring of radius $0.5\, m$ and mass $10 \,kg$ is rotating about its diameter with an angular velocity of $20 \,rad/s.$ Its kinetic energy is .......... $J$.

Two metallic spheres of equal outer radii are found to have the same moment of inertia about their respective diameters. Which of the following statement$(s)$ is/are true?

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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