A solid cylinder with mass m and radius R rolls without slipping down a plane inclined at an angle e. The coefficient of (static) friction
between the cylinder and the plane is ll. Find the linear acceleration
of the cylinder using energy conservation.

The total energy of the system is given by mohlo +mgh.

If the cylinder rolls down the slope without slipping, y = OR and a =Ra.

If it moves a distance x down the plane, its height decreases by x sin o.

Conservation of energy means dE/dt
= 0. Differentiating E,​