Analyze the moment of inertia of an object in uniformly accelerated linear motion and angular motion

Abstract

Abstract. In studying particle kinematics, calculus plays an important role in analyzing and solving motion problems as a key mathematical tool. This paper mainly discusses the application of calculus in uniformly accelerated linear motion (LM) and angular motion (AM), focusing on the relationship between position, velocity, and acceleration and the analysis of the rate of change of motion. Through the study of uniformly accelerated LM, this paper guides researchers to use calculus to establish the mathematical relationship between position, velocity, and acceleration and verifies the accuracy of these formulas through practical cases. Similarly, in AM, this paper provides an in-depth understanding of the dynamic behavior of an object rotating around a fixed axis through calculus and calculates and applies important parameters in AM to solve practical problems by analyzing angular velocity and acceleration. In addition, this paper demonstrates the potential of calculus for a wide range of applications in dealing with variable speed motion and rate of change analysis. By integrating the rate of change of displacement and acceleration, it provides a precise tool for the optimization and resolution of engineering problems. In conclusion, calculus not only enriches the theory of kinematics but also demonstrates its important value in practical applications.