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Calculate the rotational inertia of a long, thin rod of length L and mass M about one end. Assume the density of the rod is given by X. 2 = 20(1 + What is the rotational inertia (about one end) of this rod?

Calculate the rotational inertia of a long, thin rod of length L and mass M about one end. Assume the density of the rod is given by X. 2 = 20(1 + What is the rotational inertia (about one end) of this rod?

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Unless otherwise stated, assume the density is constant
**Problem Statement:** Calculate the rotational inertia of a long, thin rod of length \( L \) and mass \( M \) about one end. Assume the density of the rod is given by \[ \lambda = \lambda_0 \left(1 + \frac{x}{L}\right) \] What is the rotational inertia (about one end) of this rod? **Explanation of the Formula:** - \( \lambda \) represents the linear density of the rod, which varies along its length. - \( \lambda_0 \) is the initial linear density. - \( x \) is the position along the rod. - \( L \) is the total length of the rod. **Question:** What is the rotational inertia of this rod when rotated about one of its ends?
Transcribed Image Text:**Problem Statement:** Calculate the rotational inertia of a long, thin rod of length \( L \) and mass \( M \) about one end. Assume the density of the rod is given by \[ \lambda = \lambda_0 \left(1 + \frac{x}{L}\right) \] What is the rotational inertia (about one end) of this rod? **Explanation of the Formula:** - \( \lambda \) represents the linear density of the rod, which varies along its length. - \( \lambda_0 \) is the initial linear density. - \( x \) is the position along the rod. - \( L \) is the total length of the rod. **Question:** What is the rotational inertia of this rod when rotated about one of its ends?
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