Techno Linear Motion Catalog29Technical InformationWI= (r12 +r22) for a cylinder2whereW = Weight in poundsr= Radius in inchesEquivalent InertiaA motor must be able to:a. overcome any frictional load in the systemb. start and stop all inertial loads including that of its own rotorThe basic rotary relationship is:IaT = 24where:T = torque (ozin)I= moment of inertia (lb in2)a = angular acceleration, in radians per square second (rad/sec2)Angular acceleration (a) is a function of the change in velocity (w) and the time required for the change.w2w1a = tor, if starting from zero,wa = twhere:w = angular velocity (rad/sec)t = time (sec)steps per secondsince w = x 2p,steps per revolutionangular velocity and angular acceleration can also be expressed in steps per second (w') and steps persquare second (a'), respectively.Sample CalculationsA.Calculating torque required to rotationally accelerate an inertia load:w' pq1T = 2 x IO x x t180 24where:T = torque required (ozin)IO= inertial load (lb in2)p = 3.1416q = step angle (degrees)w' = step rate (steps/sec)Example:Assume the following conditions:Inertia = 9.2 lb in2Step Angle = 1.8°Acceleration = from 0 to 1000 steps per second in 0.5 secondsMotorInertial Load