A cylinder of mass 10 kg and radius 15 cm is rolling perfectly on a plane of inclination ${30}^0$. The co-efficient of static friction ${\mathrm{\mu }}_{\mathrm{k}}=0.25$. If the inclination $\mathrm{\theta }$ of the plane is increased, at what value of $\mathrm{\theta }$ does the cylinder begin to skid, and not roll perfectly?

The cylinder's mass is m = 10 kg.

The cylinder's radius is r  = 15 cm (0.15 metres).

${\mathrm{\mu }}_{\mathrm{s}}$ = 0.25 is the static friction coefficient.

Angle of inclination: $\theta ={30}^o$

For rolling without skidding in case of a cylinder to:

$\mathrm{\mu }\ge \frac{1}{3}\mathrm{tan\theta }$

$\mathrm{tan\theta }\le 3\mathrm{\mu }=3\times 0.25$

$\mathrm{\theta }\le {\tan }^{-1}(0.75)={37}^{°}$

Therefore for an angle above 37, the cylinder will start to skid.