Mass, Force, Velocity, and Acceleration
Velocity and Speed
Velocity of an object is the rate of change of its position with respect to time, i.e. . It is a vector quantity. Speed is the magnitude of velocity.
Acceleration
Acceleration of an object is the rate of change of its velocity with respect to time, i.e. . Notice that it is also a vector quantity.
World Line
A curve in galilean space which appears in some galilean coordinate system as the graph of a motion is called a world line.
Newton’s Laws
Newton's First Law
An object will not change its motion unless a force acts on it. Or equivalently, a mechanical system consists of only one point, then its acceleration in an inertial coordinate system is equal to zero.
Thrm Newton’s Second Law The time rate of change of the momentum of a body is equal in both magnitude and direction to the force imposed on it:
Thrm Newton’s Third Law When two bodies interact, they apply forces to one another that are equal in magnitude and opposite in direction.
Thrm Hooke’s Law and Stiffness Hooke’s law is an empirical law which states that the force needed to extend or compress a spring by some distance scales linearly with respect to that distance: where constant is called stiffness of that spring.