A cylinder of mass `m` and radius `R` rolls down an inclined plane of inclination `theta`. Calculate the linear acceleration of the axis of cylinder.

Answer

`a_("axis") = (2g sin theta)/(3)`

Explanation

For rolling without slipping, we have for translational motion

`mg sin theta - f = ma` ….(1)
for rotational motion
`R f = ((1)/(2) mR^(2)) alpha`
`f = (1)/(2) mR alpha rArr f = (1)/(2) ma`
from (1) & (2), `a = (2)/(3) g sin theta`.