Answer
The radian is defined as the ratio of the distance traveled along an arc divided by the radius of the arc. When an angle in radians is multiplied by the radius the result is a distance. Therefore, when angular speed (which is angular displacement divided by time) is multiplied by the radius the result is the displacement along the arc divided by time, which is a linear speed. degrees and revolutions are not defined in terms of arc lengths and cannot be used in the same way.
Work Step by Step
The radian is defined as the ratio of the distance traveled along an arc divided by the radius of the arc. When an angle in radians is multiplied by the radius the result is a distance. Therefore, when angular speed (which is angular displacement divided by time) is multiplied by the radius the result is the displacement along the arc divided by time, which is a linear speed. degrees and revolutions are not defined in terms of arc lengths and cannot be used in the same way.
