Question

A wheel of radius 'R' is placed on ground and its contact point is P. if wheel starts rolling without slipping and complete half of revolution ,find the displacement of point p​

Answer 1

Answer:

Displacement of p is half of its circumference which is pi *r

Answer 2

As the wheel rolls without slipping and completes a half of revolution, the initial contact point P will be at the top.

The horizontal displacement of the point P,

$\longrightarrow\vec{\sf{s_x}}=\sf{2\pi R\cdot\dfrac{\pi}{2\pi}\ \hat i}$

$\longrightarrow\vec{\sf{s_x}}=\sf{\pi R\ \hat i}$

And the vertical displacement of the point P,

$\longrightarrow \vec{\sf{s_y}}=\sf{2R\ \hat j}$

So the net displacement,

$\longrightarrow\vec{\sf{s}}=\vec{\sf{s_x}}+\vec{\sf{s_y}}$

$\longrightarrow\vec{\sf{s}}=\sf{\pi R\ \hat i+2R\ \hat j}$

$\longrightarrow\vec{\sf{s}}=\sf{R(\pi\ \hat i+2\ \hat j)}$

whose magnitude is,

$\sf{\longrightarrow s=R\sqrt{\pi^2+2^2}}$

$\sf{\longrightarrow\underline{\underline{s=R\sqrt{\pi^2+4}}}}$