What is the displacement of the point of a wheel initially in contact with the ground when the wheel rolls forward half a revolution ? Take the radius of the wheel as R and the x-axis as the forward direction?

What is the displacement of the point of a wheel initially in contact

1.	What is the displacement of the point of a wheel initially in contact with the ground when the wheel rolls forward half a revolution ? Take the radius of the wheel as R and the x-axis as the forward direction?
Answer» Solution :From FIGURE , during HALF REVOLUTION of the wheel , the point A covers `piR(=AC)` horizontal distance while `2R(=BC)` vertical distance so here , `P=piR, Q=2R` `:."Displacement", b=sqrt(P^(2)+Q^(2))` `=sqrt((piR^(2))+(2R)^(2))=Rsqrt(pi^(2)+4)` and `THETA =n Tan ^(-1)(Q/P)=Tan ^(-1)((2R)/(piR))=Tan ^(-1)(2/pi)`with x-axis. i.e., Displacement has magnitude `Rsqrt(pi^(2)+4)` and makes an angle `Tan^(-1)(2/pi)`with x-axis.