Answer to Question #78262 in Mechanics | Relativity for mahima

Question

A wheel of radius R is placed on ground and its contact point is P. if the wheel is rotated without slipping and completes half a revolution, find the displacement of point p

Answer 1

Radius: R;
Rotate: φ = 180° = π;
Solution:
As the wheel rotates on the surface without sliding, the distance traveled is equal to half the length of the circle:

L=πR

This is the displacement along the x-axis:
x=L=πR
This is the displacement along the y-axis:
y=R(cos⁡(0)-cos⁡(π))=2R
Answer:
Offset along the axis of motion: x=πR;

Height Offset: y=2R;
Point P describes a cycloid.