The cylinder rolls without slipping from an inclined plane with an angle of 30 degrees at the base.

The cylinder rolls without slipping from an inclined plane with an angle of 30 degrees at the base. Calculate the acceleration of the cylinder’s center of mass.

According to the law of conservation of energy m * g * h = m * V ^ 2/2 + J * w ^ 2/2 (1) J = m * R ^ 2/2 (2) w ^ 2 = V ^ 2 / R ^ 2 (3) Substitute 2 and 3 into 1: m * g * h = m * V ^ 2/2 + m * V ^ 2/4 = 3 * m * V ^ 2/4 g * h = 3 * V ^ 2/4 (4) h = L * sina (5) V ^ 2 = 2 * a * L (6) Substitute 5 and 6 in 4 and express a: a = 2 * g * sina / 3 = 2 * 10 * 0.5 / 3 = 3.3 m / s2