Physics · Ch 5 — Motion of System of Particles and Rigid Bodies
Comparison of Translational and Rotational Quantities
Comparison of Translational and Rotational Quantities
Many of the rotational quantities developed across §5.2 and §5.5 have expressions that are structurally identical to their translational-motion counterparts, differing only in which symbols are used. This section-long parallel is drawn together explicitly in the comparison table below, which lines up every major translational quantity against its exact rotational equivalent — displacement against angular displacement, velocity against angular velocity, acceleration against angular acceleration, mass against moment of inertia, force against torque, linear momentum against angular momentum, impulse against angular impulse, work against rotational work, kinetic energy against rotational kinetic energy, and power against rotational power. …
| Translational Motion | Rotational Motion about a Fixed Axis |
|---|---|
| Displacement, x | Angular displacement, theta |
| Time, t | Time, t |
| Velocity, v = dx/dt | Angular velocity, omega = dtheta/dt |
| Acceleration, a = dv/dt | Angular acceleration, alpha = domega/dt |
| Mass, m | Moment of inertia, I |
| Force, F = ma | Torque, tau = I alpha |
| Linear momentum, p = mv | Angular momentum, L = I omega |
| Impulse, F delta-t = delta-p | Angular impulse, tau delta-t = delta-L |
| Work done, w = F s | Work done, w = tau theta |