New acceleration analysis of rotating point in mechanics

Abstract

The velocity of a moving point in a general path is the vector quantity, which has both magnitude and direction. The magnitude and the direction of the velocity vector can change over time as a result of acceleration that the time rate of velocity changes. Acceleration analysis is important because inertial forces and inertial torque are proportional to rectilinear and angular accelerations accordingly. The loads must be determined in advance to ensure that a machine is adequately designed to handle these dynamic loads. For planar motion, the vector direction of acceleration is commonly separated into two elements: tangential and centripetal or radial components of a point on a rotating body. All fundamental textbooks in physics, kinematics and dynamics of machinery consider the magnitude of a radial acceleration at condition when a point rotates with a constant angular velocity and it means without acceleration. The magnitude of the tangential acceleration considered on a basis of acceleration for a rotating point. Such presentation of magnitudes for two components of an absolute acceleration logically and mathematically is not correct and cause confusion in calculation. This paper presents new analytical expressions of the radial and absolute accelerations of a rotating point with acceleration and covers the gap in fundamental study of acceleration analysis.