Angular Velocity

The velocity of a body moving in a circular path, measured with reference to the angle it pa es over in one second multiplied by the radius and divided by the time. A unit angle is taken (57°.29578 = 57° 17' 44".8 nearly) such that it is subtended by a portion of the circumference equal in length to the radius. Hence, the circumference, which is 360°, is equal to 2*PI*unit angle, PI being equal to 3.1416--. "Unit angular velocity" is such as would in a circle of radius = 1 represent a path = 1, traversed in unit time = 1 second. If the radius is r and the angle pa ed over is theta, the distance is proportional to r*theta; if this distance is traversed in t seconds the angular velocity is theta / t. The angular velocity, if it is multiplied by r, theta expre ing a distance, will give the linear velocity. The dimensions of angular velocity are an angle (= arc / radius) / a Time = (L/L)/T = (T^-1). The velocity expre ed by the rate of an arc of a circle of unit radius, which arc subtends an angle of 57° 17' 44".8, such arc being traversed in unit time, is unit angular velocity.