The Insect's Ride Home
An Insect is standing still on top of a Garden Roller (a Solid Cylinder) of Radius R = 1m . But unfortunately, someone pushed the Roller such that it is rolling without Slipping . Find the distance traveled ( in meters ) by the Insect in one Complete Rotation of the Roller (in the Ground Frame of Reference).
Note: Assume that the Insect is strong enough to hold on to its position at all times.
The answer is 8.
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Well, this question is almost the same as this one .
The path of the insect is a cycloid whose arc length corresponding to one revolution is 8 R .
The answer is : 8 R