Question

(i)              Calculate the angular moment of the object. When an object with the moment of inertia I = 5 kg.m² is made to rotate 1 rad/sec speed.

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Answer 1

$\\ \\ \\ \sf{\underline{\underline{ \purple{ \huge{Given:}}}}}$

✰ The moment of inertia, I = 5 kg.m²

✰ Angular velocity = 1 rad/sec

$\\ \\ \\ \sf{\underline{\underline{ \purple{ \huge{To \: Find:}}}}}$

✠ The angular momentum of the object.

$\\ \\ \\ \sf{\underline{\underline{ \purple{ \huge{Solution:}}}}}$

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⇾ The object which is rotated about a fixed point as here the object rotates about a fixed point, so it is extended object.

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Here, the angular momentum is given by,

$\blue \bigstar{\large{\green{ \underline{ \boxed{ \sf{ \ \vec{L} = I \times \vec{\omega }}}}}}}$

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Where,

• $\sf\vec{L} \: is \: the \: angular \: momentum$
• $\sf I \: is \: the \: moment \: of \: inertia$
• $\sf{ \vec{ \omega}} \: is \: the \: angular \: velocity$

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Putting the values in the formula,

$\implies \sf{ L = I \: \omega}$

$\\ \\ \implies \sf5 \: kg. {m}^{2} \times 1 \: rad/sec$

$\\ \\ {\blue {\implies{ \sf5kg. {m}^{2}. {s}^{ - 1}}}}$

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∴ The angular momentum of the object = $\green { \underline{\boxed{\sf5kg. {m}^{2}. {s}^{ - 1}}}}$

$\\ \\ \\ \sf{\underline{\underline{ \purple{ \huge{More:}}}}}$

• Angular momentum is the property of any object that is given by the product of moment of inertia and angular velocity.
• It is the property of rotating body that means the body which is rotating.

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