Displacement is the straight-line distance between initial and final positions (a vector).
Distance is the length of the path followed (a scalar).
Speed is the rate of covering distance (scalar). Velocity is speed with direction (vector).

Circular Motion (Detailed)

For rotational motion with constant angular acceleration:

$\omega = \omega_0 + \alpha t$ $\theta = \omega_0t + \frac{1}{2}\alpha t^2$ $\omega^2 = \omega_0^2 + 2\alpha\theta$

Relationships:

Angular velocity (rad/s) relates to revolutions per minute (rpm): $\omega = \frac{2\pi n}{60}$
Tangential velocity at radius $r$ : $v = \omega r$
Angular acceleration: $\alpha = \frac{d\omega}{dt} = \frac{d^2\theta}{dt^2}$
Torque: $T = \alpha I$ (where $I$ is moment of inertia)

Example Calculations

Marathon Runner Speed

A 42,195 m marathon completed in 2:03:23 (7,403 seconds): $v = \frac{42,195 \text{ m}}{7,403 \text{ s}} = 5.7 \text{ m/s} = 20.5 \text{ km/h}$

Car Acceleration

Car accelerates from 0 to 100 km/h in 10 seconds: $a = \frac{(100 \text{ km/h} \times \frac{1000}{3600} \text{ m/s}) - 0}{10 \text{ s}} = 2.78 \text{ m/s}^2$

Bicycle Tire Tangential Velocity

26-inch wheel rotating at $\pi$ rad/s: $v = \omega r = (\pi \text{ rad/s}) \times (13 \text{ in}) = 40.8 \text{ in/s}$

Flywheel Deceleration

Slowing from 2000 rpm to 1800 rpm in 10 s: $\alpha = \frac{(2000 - 1800) \text{ rev/min} \times 0.01667 \text{ min/s} \times 2\pi \text{ rad/rev}}{10 \text{ s}} = 2.1 \text{ rad/s}^2$

References

Original Source

Source: engineeringtoolbox.com