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?

Explanation

From Fig. 5.68, during half revolution of the wheel initially in contact with the ground when the wheel rolls forward half a revolution? Take the radius of the wheel the point A covers AC=`piR` in horizontal direction, and BC=2R in vertical direction.
`x=piR` and `y=2R`:
`AB=sqrt(x^(2)+y^(2))=sqrt((piR)^(2)+(2R)^(2))`
`=Rsqrt(pi^(2)+4)`

and `theta=tan^(-1)((y)/(x))=tan^(-1)((2R)/(piR))`
`=tan^(-1)((2)/(pi))` with x-axis