(Solved): A disc has radius \( r \) and mass \( m \). Derive an expression for the angu ...

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A disc has radius \( r \) and mass \( m \). Derive an expression for the angular velocity of the wheel after rolling up the step of height \( d \) if it is given an initial angular velocity \( \omega_{1} \). Use the concepts of conservation of momentum. Plot your equation for \( \omega_{2} \) as a function of the initial angular velocity \( \omega_{1} \). What are the limits of this expression? (i.e. what happens physically if \( \omega_{1} \) is too large/small).