Question

A thin cylinder starts from rest and rolls without slipping on theloop-the loop with radius R....

A thin cylinder starts from rest and rolls without slipping on theloop-the loop with radius R. Find the minimum starting height of the marblefrom which it will remain on the track through the loop. Assume the cylinder radius is small compared to R.

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Answer #1

Let us assume the cylinder was released from a height of h and let it has a velocity v at the top of the loop.

By the law of conservation of energy

The moment of inertia of the thin cylinder is given by

That gives us

In this rotational motion without slipping

that gives us

To stay on the top

Putting this value

That gives us the initial height

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