Lecture 5-5C: Rotational Energy and Momentum Translational Quantities Rotational Quantities Try simple substitution: m→I, v→ω m→I, v→ω These are the equivalents of kinetic energy and momentum for rotation I translation of rotation around center of mass center of mass Translational Work: Rotational Work: Rotational Potential Energy Conservative torques store energy as rotational potential energy Example: torsional spring on a mouse trap Conservation of Total Mechanical Energy In the absence of any dissipative forces OR torques: energy can be exchanged within system Otherwise, energy is typically lost to dissipative interactions: net dissipative net torque generated force by dissipative forces Angular Momentum Define Angular Momentum: (units: kg m2/s) Translation Rotation momentum & force impulse Conservation of Angular Momentum In the absence of any external torques on a system: Angular momentum within a system can be exchanged between components, but total angular momentum cannot be lost or gained without external torques Example: Ice Skater Spin An ice skater (or diver or gymnast) can spin their bodies faster by reducing their moment of inertia Example: Earth-Moon System Due to its tidal bulge, the Earth and Moon exert net torques on each other: The result: leap seconds Roughly every other year the official time is set ahead by 1 second to adjust for the slower rotation of the Earth compared to the historical definition of the second Image credit: NIST, www.time.gov Summary Rotational equivalents of kinetic energy and momentum follow the same laws as translational motion: The total mechanical energy is the sum of KE and PE of translation and rotation, and is lost only to dissipative forces and/or torques The angular momentum of a system is conserved in the absence of external torques .