Rotational inertia and angular momentum
Rotational inertia, also called moment of inertia, measures how hard it is to change an object's rotation. It depends not only on mass but on how that mass is spread out: mass farther from the axis gives more rotational inertia. That is why a hoop is harder to start spinning than a solid disk of the same mass and radius, and why a tightrope walker carries a long pole to resist tipping. Newton's second law has a rotational form: net torque equals rotational inertia times angular acceleration. A spinning object has angular momentum, equal to its rotational inertia times its angular velocity (L = I x angular velocity), and when no outside net torque acts on it, its angular momentum is conserved. A figure skater who pulls in their arms reduces their rotational inertia, so they spin faster; stretching the arms back out slows the spin. A rolling object, like a wheel or a ball, both moves forward and spins, so its kinetic energy is split between the energy of moving forward and the energy of rotating.
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