To calculate the linear velocity of a cylinder rolling down an inclined plane, the conservation of energy principle is applicable, where potential energy converts to kinetic energy. The potential energy at the top can be calculated using the formula PE = mgh, while the kinetic energy at the bottom consists of both translational and rotational components, expressed as KE = (1/2)mv^2 + (1/2)Iω^2. For a solid cylinder, the moment of inertia I is (1/2)mr^2, and the relationship between linear velocity (v) and angular velocity (ω) is v = rω. By substituting these values into the energy equations and solving for v, the linear velocity can be determined. Understanding these concepts and formulas is crucial for solving the problem effectively.
