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title: "Two masses, \\( m_1 \\) and \\( m_2 \\), are suspended on either side of a pulley with a radius \\( R \\), as shown. The heavier mass, \\( m_2 \\), is initially held at rest above the ground by a distance \\( h \\) before being released. An experimenting elephant measures that it takes an amount of time \\( t \\) for the heavier mass to hit the ground after being released.\\n(a) The pulley is an odd shape, and the elephant would like to measure its moment of inertia. Derive an algebraic expression for the moment of inertia of the pulley in terms of only quantities measured or known by the elephant (\\( m_1, m_2, R, h, t \\) and physical constants).\\n(b) How many radians has the pulley rotated from the time it was released to the time \\( m_2 \\) hit the ground? Express your answer in terms of \\( m_1, m_2, R, h \\) and physical constants."
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url: "https://nerd-notes.com/ubq/81010/"
date_modified: "2025-04-14T03:42:52+00:00"
---

# Two masses, \( m_1 \) and \( m_2 \), are suspended on either side of a pulley with a radius \( R \), as shown. The heavier mass, \( m_2 \), is initially held at rest above the ground by a distance \( h \) before being released. An experimenting elephant measures that it takes an amount of time \( t \) for the heavier mass to hit the ground after being released.\n(a) The pulley is an odd shape, and the elephant would like to measure its moment of inertia. Derive an algebraic expression for the moment of inertia of the pulley in terms of only quantities measured or known by the elephant (\( m_1, m_2, R, h, t \) and physical constants).\n(b) How many radians has the pulley rotated from the time it was released to the time \( m_2 \) hit the ground? Express your answer in terms of \( m_1, m_2, R, h \) and physical constants.

Two masses, \( m_1 \) and \( m_2 \), are suspended on either side of a pulley with a radius \( R \), as shown. The heavier mass, \( m_2 \), is initially held at rest above the ground by a distance \( h \) before being released. An student measures that it takes an amount of time \( t \) for the heavier mass to hit the ground after being released.

**Part a)** The pulley is an odd shape, so the student would like to measure its moment of inertia. Derive an algebraic expression for the moment of inertia of the pulley in terms of only quantities measured or known by the student (\( m_1, m_2, R, h, t \) and physical constants). *(5 points)*

**Part b)** How many radians has the pulley rotated from the time it was released to the time \( m_2 \) hit the ground? Express your answer in terms of \( m_1, m_2, R, h, t\) and physical constants. *(2 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/81010/*