Question

Derive l=Iw for a rigid body

Answer 1

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Answer 2

Answer:

The expression for the rigid body is L = I * w.

Explanation:

The angular momentum (L) of a rigid body can be calculated using the moment of inertia (I) and the angular velocity (w) using the equation L = I * w.

The moment of inertia is a measure of a body's resistance to rotational motion about a particular axis and is calculated as the sum of the product of the mass of each particle in the body and the square of its distance from the axis of rotation.

The angular velocity is a measure of the rate of change of angular displacement of a body and is typically measured in radians per second.

So, in summary, L = I * w expresses the relationship between the angular momentum of a rigid body, its moment of inertia, and its angular velocity.

$L = L_{1} + L_{2} + ... + L_{n}\\\\L = m_{1}r_{1}^2\omega + m_{2}r_{2}^2\omega + ....+ m_{n}r_{n}^2\omega\\\\L = (m_{1}r_{1}^2 + m_{2}r_{2}^2 + ....+ m_{n}r_{n}^2)\omega\\\\\therefore L = I\omega\\\\where, I = m_{1}r_{1}^2 + m_{2}r_{2}^2 + ....+ m_{n}r_{n}^2$

Hence, angular momentum = moment of inertia + angular velocity.

To learn more about the moment of inertia, click on the link below:

https://brainly.in/question/14617883

To learn more about angular momentum, click on the link below:

https://brainly.in/question/47853207

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