(B) Given: Moment of inertia $I = 1.2 \; kg \cdot m^2$,initial angular velocity $\omega_0 = 0$,rotational kinetic energy $K_r = 1500 \; J$,and angular

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(B) Given: Moment of inertia $I = 1.2 \; kg \cdot m^2$,initial angular velocity $\omega_0 = 0$,rotational kinetic energy $K_r = 1500 \; J$,and angular acceleration $\alpha = 25 \; rad/s^2$.The formula for rotational kinetic energy is $K_r = \frac{1}{2} I \omega^2$.Substituting the values: $1500 = \frac{1}{2} \times 1.2 \times \omega^2$.$1500 = 0.6 \times \omega^2 \Rightarrow \omega^2 = \frac{1500}{0.6} = 2500$.Thus,the final angular velocity $\omega = \sqrt{2500} = 50 \; rad/s$.Using the kinematic equation for rotation: $\omega = \omega_0 + \alpha t$.$50 = 0 + 25 \times t$.$t = \frac{50}{25} = 2 \; s$.

Class 11 Physics System of Particles and Rotational Motion Relation between Torque and Angular acceleration and it's Application

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The moment of inertia of a body about a given axis is $1.2 \; kg \cdot m^2$. Initially,the body is at rest. In order to produce a rotational kinetic energy of $1500 \; J$,an angular acceleration of $25 \; rad/s^2$ must be applied about that axis for a duration of: (in $; s$)

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System of Particles and Rotational Motion

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Relation between Torque and Angular acceleration and it's Application

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The moment of inertia of a body about a given axis is $1.2 \; kg \cdot m^2$. Initially,the body is at rest. In order to produce a rotational kinetic energy of $1500 \; J$,an angular acceleration of $25 \; rad/s^2$ must be applied about that axis for a duration of: (in $; s$)

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The moment of inertia of a body about a given axis is $2.4 \, kg \cdot m^2$. For what duration of time must an angular acceleration of $5 \, rad/s^2$ be applied about this axis to generate a rotational kinetic energy of $750 \, J$? (in seconds)

$A$ solid sphere of mass $2 \,kg$ and radius $1 \,m$ is free to rotate about an axis passing through its centre. $A$ constant tangential force $F$ is required to rotate the sphere with $10 \,rad/s$ in $2 \,s$ starting from rest. The value of $F$ is . . . . . . (in $\,N$)

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