Rotaatioenergia

Rotaatioenergia is the rotational kinetic energy of an object, i.e., the portion of its kinetic energy that arises from rotation about an axis. For a rigid body rotating with angular velocity ω about a fixed axis, the rotational energy is given by E_rot = 1/2 I ω^2, where I is the moment of inertia of the body with respect to that axis. The moment of inertia depends on how mass is distributed relative to the axis, with I = Σ m_i r_i^2 for discrete masses or I = ∫ r^2 dm for continuous bodies. Standard examples include a solid disk with I = 1/2 M R^2 and a thin ring with I = M R^2.

Rotaatioenergia is related to angular momentum L by L = I ω. The energy can be viewed as the work required to accelerate the rotation, since dE_rot = τ dθ where τ is the external torque and dθ is the rotation angle. In general motion, the total kinetic energy is E = 1/2 M v_cm^2 + 1/2 I_cm ω^2, with the second term being the rotational part about the center of mass. When rotation occurs about a fixed axis and the center of mass is at rest, E = 1/2 I ω^2.

Rotaatioenergia has practical significance in engineering and physics. It is the energy stored in flywheels and rotors, influences the dynamics of planets and galaxies, and is a key consideration in motors, turbines and driving mechanisms. The concept is frame-dependent: energy values depend on the chosen reference frame, while angular momentum is intrinsic to the rotation.