Displacement of a point on a rolling wheel
Help with physics problem and solution
A wheel with radius R = 10.0cm rolls without slipping on a horizontal floor. At time t0 the point P (see Figure) is touching the floor. At time t1 the wheel has rolled through a full revolution. What is the displacement of point P during this time interval?
Solution:
We must remember that displacement is a vector with magnitude equal to the distance between initial and final position and with direction from initial to final position. Therefore the displacement in this case is a vector ( red on the Figure).
The magnitude of displacement is
d = 2πR = 2π*0.1m = 0.628m (1)
because the wheel makes one revolution so this point has moved by the circumference of the wheel.
The direction is parallel to the floor.