A wheel of radius 1 meter rolls forward half a revolution on a horizontal ground. The magnitude of the displacement of the point of the wheel initially in contact with the ground is ?

1 Answer
Truong-Son N.
Jul 6, 2015

The word "initially" is important here. If we were examining the point of the wheel in contact with the ground, the displacement would be zero. Instead, we are looking at how far (straight) a point has moved after a #pi# radians revolution.

The magnitude of the point's displacement is related to the arc length of half a revolution, i.e. half a circumference.

At half a circumference of travel, the displacement is #2r# upwards.

#D = 2(1) = 2 "m"#

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