Relative velocity is the velocity of an object as observed from a particular reference frame, or the velocity of one reference frame with respect to another reference frame. The concept of relative velocity can be used to describe motion in two dimensions. Consider a particle P and two reference frames S and S′. The position of the origin of S′ as measured in S is , the position of P as measured in S′ is , and the position of P as measured in S is , which can be evaluated by...

Motion draws our attention. Motion itself can be beautiful, causing us to marvel at the forces needed to create spectacular sights, such as that of a dolphin jumping out of the water, the flight of a bird, or the orbit of a satellite. The study of motion is kinematics, but kinematics only describes the way objects move—their velocity and acceleration. Dynamics considers the forces that affect the motion of moving objects and systems. Newton's laws of motion are the foundation of...

A rigid body is said to be in dynamic equilibrium when both its linear and angular acceleration are zero, relative to an inertial frame of reference. This means that a body in equilibrium can be moving, but only when its linear and angular velocities are constant. A rigid body is said to be in static equilibrium when it is at rest in the selected frame of reference. The distinction between static equilibrium (e.g., a state of rest) and dynamic equilibrium (e.g, a state of uniform motion) is...

In 1905, Albert Einstein published his special theory of relativity. According to this theory, no matter in the universe can attain a speed greater than the speed of light in a vacuum, which thus serves as the speed limit of the universe.
This has been verified in many experiments. However, space and time are no longer absolute. Two observers moving relative to one another do not agree on the length of objects or the passage of time. The mechanics of objects based on Newton's laws of...

The torque-free motion refers to the movement of a rigid body in space when no external torques are acting upon it. This type of motion can be observed in environments where there are no external forces or frictions, like in outer space. For example, a rotation of Mars in space is a torque-free motion. Mars is an axisymmetric object, meaning it has an axis of symmetry along which it rotates, designated as the z-axis. The rotating frame of reference is defined such that the center of mass of...

In classical mechanics, motion is often described through relationships between spatial coordinates and time. A car moving along a straight highway with constant acceleration serves as a simple case where velocity is an explicit function of time. This scenario results in a linear equation, enabling straightforward analysis using basic differentiation techniques.In contrast, a satellite in circular orbit follows a path defined by an implicit function. The position of the satellite is constrained...