AP Physics 1
6.5 Rolling
6.1 Rotational Kinetic Energy
3.4 Conservation of Energy
3.3 Potential Energy
3.2 Work
3.1 Translational Kinetic Energy
2.9 Circular Motion
Multi-Unit

In the figure above, the marble rolls down the track and around a loop-the-loop of radius \( R \). The marble has mass \( m \) and radius \( r \). What minimum height \( h_{min} \) must the track have for the marble to make it around the loop-the-loop without falling off? Express your answer in terms of the variables \( R \) and \( r \).
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