The angular speed of a body of flexible shape is halved, without applying any external torque. Find the factor by which its rotational kinetic energy would change.
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When external torque is not applying . It means angular momentum of system is conserved . And we know, angular momentum ( L ) = Iω
Where I is moment of inertia of body with respect axis of rotation of body and ω is angular velocity of body .
And rotation kinetic energy = 1/2 Iω² = 1/2{Iω}²/I = L²/2I, hence, rotational kinetic energy = L²/2I , here it is clear that rotational Kinetic energy depends upon angular momentum and moment of inertia in case of external torque = 0
Now, your question said , angular speed is halved . But our rotational Kinetic energy independent upon angular speed . So, there won't any change in rotational Kinetic energy if angular speed is changed in case of eternal torque = zero.
hence, answer is rotational Kinetic energy will remain same.
Where I is moment of inertia of body with respect axis of rotation of body and ω is angular velocity of body .
And rotation kinetic energy = 1/2 Iω² = 1/2{Iω}²/I = L²/2I, hence, rotational kinetic energy = L²/2I , here it is clear that rotational Kinetic energy depends upon angular momentum and moment of inertia in case of external torque = 0
Now, your question said , angular speed is halved . But our rotational Kinetic energy independent upon angular speed . So, there won't any change in rotational Kinetic energy if angular speed is changed in case of eternal torque = zero.
hence, answer is rotational Kinetic energy will remain same.
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