Question #78262
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
Expert's answer
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.
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.
