Question

Derive an expression for acceleration and force of friction experienced by a solid cylinder rolling down an inclined plane of inclination $\theta$ with the horizontal.

Answer 1

We have,

$mg\sin \theta -f=ma...........\left(1\right)$

$fR=\frac{M{R}^2}{2}.\alpha .........\left(2\right)$

$a=\alpha R...................\left(3\right)$

From (2) & (3)

$fR=\frac{M{R}^2}{2}\times \frac{\alpha }{R}$

$\Rightarrow fR=\frac{Ma}{2}.........\left(4\right)$

From $\left(1\right)$ & $\left(4\right)$

$mg\sin \theta -\frac{ma}{2}=ma$

$\Rightarrow mg\sin \theta =\frac{3ma}{2}$

$\begin{array}{c}a=\frac{2g\sin \theta }{3}\\ f=\frac{mg\sin \theta }{3}\end{array}$