Question

Consider a wheel of a bicycle rolling on a level road at a linear speed ${\nu }_0$ (figure 10-Q5).
(a) the speed of the particle A is zero
(b) the speed of B, C and D are all equal to $v_0$
(c) the speed of C is 2 $v_0$
(d) the speed of B is greater than the speed of O.
Figure

Answer 1

(a) the speed of the particle A is zero
(c) the speed of C is 2 $v_0$
(d) the speed of B is greater than the speed of O

For pure rolling, $\omega r=v_0$
Velocity of the particle at A, B, C and D will be resultant of v₀ and ωr.



At point B,
$$\begin{gathered} v_{net}=\sqrt{{v_0}^2+{\left(\omega r\right)}^2} \\ {v}_{net}=\sqrt{{v_0}^2+{v_0}^2} \\ {v}_{net}=\sqrt{2}{v}_0 \end{gathered}$$

At point C,
$$\begin{gathered} v_{net}=v_0+\left(\omega r\right) \\ {v}_{net}=2v_0 \end{gathered}$$

At point A,
$$\begin{gathered} v_{net}=v_0-\left(\omega r\right) \\ {v}_{net}=0 \end{gathered}$$

At point O,
r = 0
$\therefore v_{net}=v_0$