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The text says that
To Explain:The different forms of the angular momentum mathematically.
Explanation of Solution
Introduction:
Spinning of top is the best example of rotational dynamics. In rotational dynamic motion of the body represented by the angular momentum. Angular momentum is the vector quantity and denoted by symbol L . Angular momentum of the body about the center of rotation is,
Where,
Suppose body is moving along the circular path having velocity
Similarly, for the rigid body rotating about an axis, particle of the rigid body moving along the circle of the radius r with angular velocity
Linear velocity due to the motion of the particle is,
From equation (1), Angular momentum can be written as,
Where,
Conclusion: Equation (1) and equation (2) are the same but represents differently. Depending on the situation of the problem equation (1) or (2) can be used.
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