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