The speed of a point on the circumference depends on its distance from the centre of the circle.

Let's assume the circle has a radius of $r$ m. Then, its circumference is $2{\pi}r$ m. If it rotates at 1 rpm, a point on the circumference will travel the whole circumference, or $2{\pi}r$ m, in 1 second. During that second it will also travel $360^{\circ}$, or $2\pi$ radians.

Hence angle*radius/second corresponds to metre/second.

The speed of a point on the circumference depends on its distance from the centre of the circle.

Let's assume the circle has a radius of $r$ m. Then, its circumference is $2{\pi}r$ m. If it rotates at 1 rpm, a point on the circumference will travel the whole circumference, or $2{\pi}r$ m, in 1 second. During that second it will also travel $360^{\circ}$, or $2\pi$ radians.

Angles are dimensionless and hence angle*radius/second corresponds to metre/second.