Question

Consider a bicycle tyre rolling without slipping on a smooth horizontal surface with a linear velocity $v_0$ as shown in figure. Then, which of the following statement is incorrect?

• A. Speed of point $A$ is zero
• B. Speed of point $B,C$ and $D$ are equal to $v_0$
• C. Speed of point $B>$ speed of point $O$
• D. Speed of point $C=2v_0$

Answer 1

The correct option is B Speed of point $B,C$ and $D$ are equal to $v_0$

Let the radius of bicycle wheel be $r$
For rolling without slipping $v_0=r\omega$
$\Rightarrow$ Net velocity of any point on the bicycle wheel will be a vector sum of translational velocity and tangential velocity due to rotational motion, at that point.


We can see that at point $B$ and $D$, $\Rightarrow {\overrightarrow{v}}_B,{\overrightarrow{v}}_D$ will be greater in magnitude compared to ${\overrightarrow{v}}_0$, since taking resultant of velocities, $\theta <{90}^{\circ },\cos \theta \text{is}+ve$ hence component vectors will add up together at points $B$ and $D$ to yield a higher velocity than ${\overrightarrow{v}}_0$

$\Rightarrow$At point $C$ net speed is :
$|{\overrightarrow{v}}_C|=v_0+r\omega =2v_0$
$\Rightarrow$At point $A$ net speed is :
$|{\overrightarrow{v}}_A|=v_0-r\omega =v_0-v_0=0$ $\because v_0=r\omega$

$\therefore$ Option $\left(b\right)$ is incorrect