Fig. shows a disc rolling on a horizontal plane with linear velocity $\mathrm{v}$. Its linear velocity is…
Fig. shows a disc rolling on a horizontal plane with linear velocity $\mathrm{v}$. Its linear velocity is $\mathrm{v}$ and angular velocity is $\omega$. Which of the following gives the velocity of the particle $P$ on the rim of the disc?
$v(1+\cos \theta)$
$v(1-\cos \theta)$
$v(1+\sin \theta)$
$v(1-\sin \theta)$
Solution
Velocity of $\mathrm{P}=(\mathrm{NP}) \omega=(\mathrm{NM}+\mathrm{MP}) \omega$
$=\mathrm{r}(\mathrm{r}+\sin \theta) \omega=\mathrm{v}(1+\sin \theta)$
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