Torque and Angular Acceleration

A calculus based approach to electric motor dynamics

Abstract

The general behaviour of electric motors is highly dependent on mechanical load, developed torque, and angular acceleration. This paper presents a calculus-based analysis of motor dynamics using differential equations as the main mathematical modelling framework. Starting from Newton's second law for rotational motion, a first-order differential equation is derived to describe angular velocity as a function of time. The effects of load torque, viscous friction, and rotor inertia are included to produce a practical motor model. The solution of the differential equation gives insight into both transient and steady-state motor behaviour, forming a foundation for modern electric-drive analysis, mechatronic system design, and motor control.