A lawn roller in the form of a thin-walled hollow cylinder of mass M is pulled
horizontally with a constant force F applied by a handle attached to its axle. If it rolls
without slipping, find the acceleration and the friction force ?

Explanation:

If '' be the mass of the roller and '' is the radius of its cylindrical shape, then moment of inertia '' can be written as,

If '' is the force by which the roller is pulling, '' is the frictional force and '' is the acceleration generated in the roller, then considering the linear motion of the roller, we can write

Considering the rolling motion of the roller, if '' be the angular velocity of the roller, then frictional force '' due to rolling is

where, '' is the angular acceleration.

According to the problem, . Therefore,

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s