Final answer:
The rotational kinetic energy of a thin rod rotating in a horizontal plane can be calculated using the formula: Rotational kinetic energy (KEr) = (1/2) * Moment of inertia (I) * Angular velocity (ω)^2.
Step-by-step explanation:
The rotational kinetic energy of a thin rod rotating in a horizontal plane about a vertical axis passing through its one end can be calculated using the formula:
Rotational kinetic energy (KEr) = (1/2) * Moment of inertia (I) * Angular velocity (ω)2
The moment of inertia (I) for a thin rod rotating about an axis perpendicular to its length and passing through its center is given by:
Moment of inertia (I) = (1/12) * mass of rod (M) * length of rod (L)2
Substituting the given values of the cross-sectional area (A) and density (ρ), the mass of the rod (M) can be calculated as:
Mass of rod (M) = A * length of rod (L) * density (ρ)
Therefore, the rotational kinetic energy of the rod can be calculated using the above formulas and the given values of length (l), angular velocity (ω), cross-sectional area (A), and density (ρ).