(B) The rotational kinetic energy is given by $K = \frac{1}{2} I \omega^2$.Given $K = 1500 \ J$ and $I = 1.2 \ kg \cdot m^2$,we have:$1500 = \frac{1}{

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(B) The rotational kinetic energy is given by $K = \frac{1}{2} I \omega^2$.Given $K = 1500 \ J$ and $I = 1.2 \ kg \cdot m^2$,we have:$1500 = \frac{1}{2} \times 1.2 \times \omega^2$$1500 = 0.6 \times \omega^2$$\omega^2 = \frac{1500}{0.6} = 2500$$\omega = 50 \ rad/s$.Since the body starts from rest,the initial angular velocity $\omega_0 = 0$.Using the equation of motion $\omega = \omega_0 + \alpha t$,where $\alpha = 25 \ rad/s^2$:$50 = 0 + 25 \times t$$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. To produce a rotational kinetic energy of $1500 \ J$,an angular acceleration of $25 \ rad/s^2$ must be applied to the body for a duration of ........ $(s)$.

A
$4$
B
$2$
C
$8$
D
$10$

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System of Particles and Rotational Motion

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Relation between Torque and Angular acceleration and it's Application

One end of a rod is hinged at $O$. The other end is suspended by a string attached to the ceiling as shown in the figure. If the string is suddenly cut,find the angular acceleration of the rod.

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$A$ thin uniform hemispherical bowl of mass $m$ and radius $R$ is lying on a smooth horizontal surface. $A$ horizontal force $F$ is now applied perpendicular to the rim of the bowl (see figure). The instantaneous angular acceleration of the bowl will be

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$A$ disc has mass $M$ and radius $R$. How much tangential force should be applied to the rim of the disc so as to rotate the disc with angular velocity $\omega$ in time $t$?

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$A$ rod $PQ$ of mass $M$ and length $L$ is hinged at end $P$. The rod is kept horizontal by a massless string tied to point $Q$ as shown in the figure. When the string is cut,the initial angular acceleration of the rod is

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If $I$,$\alpha$,and $\tau$ are the moment of inertia,angular acceleration,and torque of an object,respectively,and the object is rotating about an axis with an angular velocity $\omega$,then:

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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. To produce a rotational kinetic energy of $1500 \ J$,an angular acceleration of $25 \ rad/s^2$ must be applied to the body for a duration of ........ $(s)$.

Similar Questions

One end of a rod is hinged at $O$. The other end is suspended by a string attached to the ceiling as shown in the figure. If the string is suddenly cut,find the angular acceleration of the rod.

$A$ thin uniform hemispherical bowl of mass $m$ and radius $R$ is lying on a smooth horizontal surface. $A$ horizontal force $F$ is now applied perpendicular to the rim of the bowl (see figure). The instantaneous angular acceleration of the bowl will be

$A$ disc has mass $M$ and radius $R$. How much tangential force should be applied to the rim of the disc so as to rotate the disc with angular velocity $\omega$ in time $t$?

$A$ rod $PQ$ of mass $M$ and length $L$ is hinged at end $P$. The rod is kept horizontal by a massless string tied to point $Q$ as shown in the figure. When the string is cut,the initial angular acceleration of the rod is

If $I$,$\alpha$,and $\tau$ are the moment of inertia,angular acceleration,and torque of an object,respectively,and the object is rotating about an axis with an angular velocity $\omega$,then:

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