Question

is friction necessary for a body to roll? what is the minimum friction required for a disc of mass M and radius r to roll in an inclined plane

Answer 1

$$\begin{gathered} Dearstudent \\ Yes,frictionisrequiredforrollingotherwisebodywouldslip \\ foradiscrollingdownaplane \\ f-mg\sin \theta =ma \\ fisfric \\ \theta isangleofincline \\ writingtorqueequation \\ fr=I\alpha \\ fr=\frac{1}{2}m{r}^2\alpha \\ forpurerolling, \\ a=r\alpha \\ so, \\ fr=\frac{1}{2}m{r}^2\alpha \\ fr=\frac{1}{2}m{r}^2\frac{a}{r} \\ fr=\frac{1}{2}mra \\ \frac{2}{m}f=a \\ so, \\ f-mg\sin \theta =ma \\ f-mg\sin \theta =m\frac{2}{m}f \\ f-mg\sin \theta =2f \\ f=mg\sin \theta \\ Regards \end{gathered}$$note, symbols have usual meanings