Arc Length, Angular + Linear Velocity

A portion of the circumference

of a circle

distance across a circle

distance from center

of circle to edge

distance around the circle

the angle made

between 2 radii

How fast a circle spins

Rate of change of the angle with respect to time

The abstraction of your thoughts

The speed of an object along the circumference of a circle

How fast the angle changes

The distance in a straight line of the circumference

An extraneous value unrelated to the problem

$$s=\pi r^2$$

$$s=2\pi r$$

$$s=r\theta$$

$$s=r^2-\pi\theta$$

Revolutions per radians

$$w=2\pi r$$

$$w=r\theta$$

$$w=\frac{\theta}{t}$$

$$v=\frac{s}{t}$$

$$v=\frac{r\theta}{t}$$

$$v=rw$$

$$v=2\pi r\theta$$

$$v=\frac{\theta}{t}$$

3π/4 ft

39π/4 ft

13π/4 ft

4π/13 ft