91影视

The velocity on the point of a rim of the wheel is given by,

$\mathit{v}\mathbf{=}{\mathit{V}}_{\mathbf{C}}\mathit{M}\mathbf{+}\mathit{蝇}\mathit{R}\mathbf{(}\mathbf{-}\mathit{c}\mathit{o}\mathit{s}\mathbf{}\mathit{胃}{\mathit{e}}_{\mathbf{x}}\mathbf{+}\mathit{s}\mathit{i}\mathit{n}\mathbf{}\mathit{胃}{\mathit{e}}_{\mathbf{y}}\mathbf{)}$ (1)

Where$蝇$ angular speed of the wheel is,R is its radius and$V_{CM}$ is the velocity of its center of mass.

We have given that A wheel is rolling without slipping on a horizontal surface.

Assuming$V_{CM}=v_{cm}{e}_x$

So, from equation (1) we can write,

$v=(v_{CM}-蝇Rcos胃)e_x+蝇Rsin胃e_y$

When there is no slipping we have

$v_{CM}=蝇R$

So, we get

$v=(蝇R-蝇Rcos胃)e_x+蝇Rsin胃e_y$

Now, if velocity is purely vertical. Then,

$$\begin{gathered} 蝇R\left(1-\cos 胃\right)=0 \\ \cos 胃=1 \\ 胃=0 \end{gathered}$$

However, when$胃=0$ the vertical component of the velocity is zero.

Since$蝇R\sin 胃=0$

We can conclude that there is no point on the wheel that has a purely vertical velocity.

The horizontal velocity component opposite to the velocity of the center of mass when

$$\begin{gathered} 1-\cos 胃=0 \\ \cos 胃>1 \end{gathered}$$

This can never be satisfied.

So, there is no point that has a horizontal velocity component opposite to the velocity of the center of mass.

When there is slipping the condition$v_{CM}=蝇R$ is not satisfied.

In this case we have,$v_{CM}>蝇R$

In this case the horizontal components of the velocity is never zero which means the velocity is never purely in the vertical direction.