Work, Energy And Power For Rotating Body - Practice Questions & MCQ
Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main
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16 Questions around this concept.
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EASYIf 'I' is the moment of inertia of a body and 'w' is its angular velocity, the rotational kinetic energy of the body is
A body of M.I. 3 kg $m^2$ rotating with an angular velocity 2 rad/s has the same K.E. as a mass of 12 kg moving with a velocity of
A thin hollow sphere of mass m is completely filled with an ideal liquid of mass m. When the sphere rolls with a velocity v kinetic energy of the system is equal to
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A wheel of mass 2 kg having practically all the mass concentrated along the circumference of a circle of radius 20 cm, is rotating on its axis with an angular velocity of 100 rad/s. The rotational kinetic energy of the wheel is
Concepts Covered - 1
Work, Energy and Power for Rotating Body
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Work-
For translation motion
$
W=\int F d s
$
So for rotational motion
$
W=\int \tau d \theta
$
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Rotational kinetic energy-
The energy of a body has by virtue of its rotational motion is called its rotational kinetic energy.
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Rotational kinetic energy |
Translatory kinetic energy |
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Power =Rate of change of kinetic energy
For translation motion $P=\vec{F} \cdot \vec{V}$
So for rotational motion
$
P=\frac{d\left(K_R\right)}{d t}=\frac{d\left(\frac{1}{2} I \omega^2\right)}{d t}=I \omega \frac{d \omega}{d t}=I \alpha \omega=\tau \cdot \omega
$
Or $P=\vec{\tau} \cdot \vec{\omega}$
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