Rotational Kinetic Energy - AP Physics 1

Increases moment of inertia. More mass means greater resistance to angular acceleration.

Increases by factor of 4. Since $KE_r \propto \omega^2$, doubling speed quadruples energy.

Affects rotational stability. Spinning objects resist changes to their orientation.

Converts to thermal energy. Friction does negative work, removing rotational kinetic energy.

Changes rotational kinetic energy. Net torque changes angular velocity, altering rotational energy.

Affects moment of inertia ($I$). Different axes change how mass is distributed relative to rotation.

Joules (J). Same unit as linear kinetic energy since both measure energy.

$I = \frac{1}{2} m r^2$. Standard formula for cylinder rotating about its central axis.

Increases $KE_r$. Larger radius increases moment of inertia for given mass.

Affects moment of inertia. Different shapes distribute mass differently from rotation axis.

Thermal energy. Friction converts organized rotational motion to random molecular motion.

Both are forms of mechanical energy. Both store energy and can be converted into other energy forms.

Moment of inertia ($I$). Both represent inertia - resistance to change in motion.

Moment of inertia. Rotational analog of mass, measuring resistance to angular acceleration.

$KE + PE + KE_r = \text{constant}$. Total mechanical energy includes all kinetic and potential energies.

Moment of inertia. For rotating disk, $I$ depends on mass distribution and radius.

Angular velocity. When $I$ is constant, $KE_r$ depends only on $\omega^2$.

Decreases $KE_r$. Since $KE_r \propto \omega^2$, smaller $\omega$ means less energy.

Affects change in $KE_r$. Angular acceleration changes $\omega$, thus changing energy.

Can increase or decrease $KE_r$. Collisions can transfer or dissipate rotational energy.

Work equals change in $KE_r$. Work-energy theorem applies to rotational motion.

Torque affects angular acceleration. Torque changes angular velocity, thus changing rotational energy.

Moment of inertia ($I$). Larger moment of inertia means more rotational kinetic energy.

Decreases angular velocity. For fixed energy, larger $I$ requires smaller $\omega$.

Increases with larger radius. Larger radius increases moment of inertia for most objects.

$I = \frac{2}{5} m r^2$. Standard formula for solid sphere rotating about diameter.

Part of total mechanical energy. Must be included when applying conservation of mechanical energy.

Affects moment of inertia ($I$). Mass farther from axis increases $I$, thus increasing rotational energy.

Affects moment of inertia ($I$). Different axes change how mass is distributed relative to rotation.