In this problem you will consider the motion of a cylinder

of radius $r_{cyl}$ that is rolled from a certain height $h$ so that

it "loops the loop," that is$,$ rolls around the track with a

loop of radius $r_{\text{l}\text{o}\text{o}\text{p}}$ shown in the figure without losing

contact with the track. $($Figure $1)$

Unless otherwise stated, assume that friction is sufficient

that the cylinder rolls without slipping. The radius $r_{cyl}$ of

the cylinder is much smaller than the radius $r_{\text{l}\text{o}\text{o}\text{p}}$ of the

loop.

Figure

Compared to an object that does not roll, but instead slides without friction, should a rolling object be released from

the same,a greater, or a lesser height in order just barely to complete the loop the loop?

The rolling object should be released from a greater height.

The rolling object should be released from a lesser height.

The rolling object should be released from exactly the same height.

The answer depends on the moment of inertia of the rolling object.

Request Answer

Part B

Find the minimum height $h$ that will allow a solid cylinder of mass $m$ and radius $r_{cyl}$ to loop the loop of radius $r_{\text{l}\text{o}\text{o}\text{p}}.$

Express $h$ in terms of the radius $r_{\text{l}\text{o}\text{o}\text{p}}$ of the loop.

$h=$