Mechanical Engineering Formulas For Motion Control
Acceleration = Final Velocity – Initial Velocity
Time
Acceleration Torque = Moment of Inertia X Angular Acceleration
The torque exerted on an object is equal to the product of that object’s moment of inertia times its angular
acceleration. The angular acceleration is in the same direction as the torque. See Inertia and F=ma.
Circumference = Diameter x Pi (3.14) or Radius x 2Pi (6.28)
F=ma (Force = mass x acceleration)
Isaac Newton’s second law of motion: the net force on an object is equal to the mass of the object multiplied by
its acceleration.
FPM (feet per minute) = RPM x Circumference in feet
Gear ratio: reduces reflected inertia by the square of the reduction
Example: If reflected inertia to the motor is 225 lb. ft.2, and a 15:1 reducer is added between the motor and the
load, the reflected inertia is reduced by a factor of 225.
15:12 = 15 x 15 = 225, Reflected Inertia = 225 lb. ft.2, = 1 lb.ft.2
225
Horsepower
A phrase coined by James Watt, the inventor of the steam engine. Horsepower is defined as work done over
time. The exact definition of one horsepower is 33,000 lb.ft./minute. Put another way, if you were to lift 33,000
pounds one foot over a period of one minute, you would have expended one horsepower of energy.
HP=
Weight x Feet Per Minute
33,000
Torque(in.lbs.) x RPM
63,025
Torque(ft.lbs.) x RPM
5,252
1 HP = 746 Watts (continuous)
DC Motor Amps x Volts x % Efficiency
746
Single Phase AC Motor Amps x Volts x Efficiency
746
3 Phase AC Motor Amps x Volts x Efficiency x Power Factor x 1.73
746
IPM (inches per minute) = PRM x Circumference in inches
Inertia and Acceleration Torque
Simplified, inertia refers to an object's amount of resistance to change in velocity. Isaac Newton stated in his
first law of motion that