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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 r-axis as the forward direction? |
Answer» Solution :From figure, during half REVOLUTION of the wheel, the point A covers `AC = pi` horizontal distance, and BC = 2R vertical distance.  `x=pi R and y=2R`. Displacement, `s= sqrt(x^(2)+y^(2))= sqrt((piR)^(2)+(2R)^(2))=R sqrt(pi^(2)+4)` and `theta =Tan^(-1)((y)/(x))= 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)/(i))` with x-axis. |
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