Question

The wheel of radius $R$ rolls without slipping on horizontal rough surface, and its centre $O$ has an horizontal acceleration $a_{0}$ in forward direction. A point $P$ on the wheel is a distance $r$ from $O$ and angular position $\theta$ from horizontal. For the given values of $a_{0}, R$ and $r$, determine the angle $\theta$ for which point $P$ has no acceleration in this position.

• A. $\cos ^{-1} \frac{r}{R}$
• B. $\tan ^{-1} \frac{r}{R}$
• C. $\sin ^{-1} \frac{r}{R}$
• D. $\cos ^{-1} \frac{r}{2 R}$

Answer 1

Answer: (C)

The acceleration of the point $P$ is due to the axis and due to rotation about the axis

$ a_{0} \cos \theta =\omega^{2} r \,\,\,...(1)$
$a_{0} \sin \theta =\alpha r \,\,\,...(2)$
and $ a_{0} =R \alpha \,\,\,...(3)$
from (2) and (3) $\sin \theta=\frac{r}{R}$
$\Rightarrow \theta=\sin ^{-1}\left(\frac{r}{R}\right)$