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A wheel rolling along a rough horizontal...

A wheel rolling along a rough horizontal surface with an angular velocity `omega` strikes a rough vertical wall, normally. Find the initial angular velocity, as it tends to roll up the wall (neglect any slippage) due to impulse.

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To solve the problem of a wheel rolling along a rough horizontal surface with an angular velocity \( \omega \) striking a rough vertical wall normally, we will use the principles of angular momentum and the conditions of pure rolling motion. Here’s a step-by-step solution: ### Step 1: Understand the System The wheel is rolling towards a vertical wall with an angular velocity \( \omega \). When it strikes the wall, it experiences an impulse that causes it to roll up the wall. We need to find the initial angular velocity as it tends to roll up. **Hint:** Visualize the wheel's motion and the forces acting on it when it strikes the wall. ### Step 2: Identify Forces and Points of Contact ...
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