Question

A wheel with a radius of 61.0 cm rolls without slipping along a horizontal floor (see the figure). At time t₁, the dot P painted on the rim of the wheel is at the point of contact between the wheel and the floor. At a later time t₂, the wheel has rolled through one-half of a revolution. What are (a) the magnitude and (b) the angle (relative to the floor) of the displacement of P during this interval?

Answer 1

Part A

If the wheel has done one half of a revolution, the angular displacement is

Therefore, the displacement of the wheel itself is the horizontal displacement of the particle

After half a rotation, the particle will move upwards, i.e it will be on the top of the wheel at a distance equal to from the floor.

This is the vertical displacement of the particle

Therefore, the displacement of the particle is

Part B