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Relative velocity is fundamental in both classical and modern physics, since many systems in physics deal with the relative motion of two or more particles.

In Newtonian mechanics, the relative velocity is independent of the chosen inertial reference frame. This is not the case anymore with special relativity in which velocities depend on the choice of reference frame.

If an object A is moving with velocity vector v and an object B with velocity vector w , then the velocity of object A relative to object B is defined as the difference of the two velocity vectors:.

Similarly, the relative velocity of object B moving with velocity w , relative to object A moving with velocity v is:. Usually, the inertial frame chosen is that in which the latter of the two mentioned objects is in rest.

In the one-dimensional case, [3] the velocities are scalars and the equation is either:. In polar coordinates , a two-dimensional velocity is described by a radial velocity , defined as the component of velocity away from or toward the origin also known as velocity made good , and an angular velocity , which is the rate of rotation about the origin with positive quantities representing counter-clockwise rotation and negative quantities representing clockwise rotation, in a right-handed coordinate system.

The radial and angular velocities can be derived from the Cartesian velocity and displacement vectors by decomposing the velocity vector into radial and transverse components.

The transverse velocity is the component of velocity along a circle centered at the origin. The magnitude of the radial velocity is the dot product of the velocity vector and the unit vector in the direction of the displacement.

The magnitude of the transverse velocity is that of the cross product of the unit vector in the direction of the displacement and the velocity vector.

Angular momentum in scalar form is the mass times the distance to the origin times the transverse velocity, or equivalently, the mass times the distance squared times the angular speed.

The sign convention for angular momentum is the same as that for angular velocity. If forces are in the radial direction only with an inverse square dependence, as in the case of a gravitational orbit , angular momentum is constant, and transverse speed is inversely proportional to the distance, angular speed is inversely proportional to the distance squared, and the rate at which area is swept out is constant.

These relations are known as Kepler's laws of planetary motion. From Wikipedia, the free encyclopedia. This article is about velocity in physics.

For other uses, see Velocity disambiguation. Vector that measures the rate of change in position over time of a moving point.

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources.

Unsourced material may be challenged and removed. As a change of direction occurs while the racing cars turn on the curved track, their velocity is not constant.

Second law of motion. History Timeline Textbooks. Newton's laws of motion. Analytical mechanics Lagrangian mechanics Hamiltonian mechanics Routhian mechanics Hamilton—Jacobi equation Appell's equation of motion Koopman—von Neumann mechanics.

Core topics. Circular motion Rotating reference frame Centripetal force Centrifugal force reactive Coriolis force Pendulum Tangential speed Rotational speed.

Main article: Speed. Main article: Equation of motion. Main article: Relative velocity. Four-velocity relativistic version of velocity for Minkowski spacetime Group velocity Hypervelocity Phase velocity Proper velocity in relativity, using traveler time instead of observer time Rapidity a version of velocity additive at relativistic speeds Terminal velocity Velocity vs.

Wolfram MathWorld. Retrieved 2 June Vector analysis: a text-book for the use of students of mathematics and physics, founded upon the lectures of J.

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In the special case of constant acceleration, velocity can be studied using the suvat equations. By considering a as being equal to some arbitrary constant vector, it is trivial to show that.

It is also possible to derive an expression for the velocity independent of time, known as the Torricelli equation , as follows:.

The above equations are valid for both Newtonian mechanics and special relativity. Where Newtonian mechanics and special relativity differ is in how different observers would describe the same situation.

In particular, in Newtonian mechanics, all observers agree on the value of t and the transformation rules for position create a situation in which all non-accelerating observers would describe the acceleration of an object with the same values.

Neither is true for special relativity. In other words, only relative velocity can be calculated. The kinetic energy of a moving object is dependent on its velocity and is given by the equation.

Kinetic energy is a scalar quantity as it depends on the square of the velocity, however a related quantity, momentum , is a vector and defined by.

In special relativity , the dimensionless Lorentz factor appears frequently, and is given by. Escape velocity is the minimum speed a ballistic object needs to escape from a massive body such as Earth.

It represents the kinetic energy that, when added to the object's gravitational potential energy, which is always negative is equal to zero.

The general formula for the escape velocity of an object at a distance r from the center of a planet with mass M is. This makes "escape velocity" somewhat of a misnomer, as the more correct term would be "escape speed": any object attaining a velocity of that magnitude, irrespective of atmosphere, will leave the vicinity of the base body as long as it doesn't intersect with something in its path.

Relative velocity is a measurement of velocity between two objects as determined in a single coordinate system. Relative velocity is fundamental in both classical and modern physics, since many systems in physics deal with the relative motion of two or more particles.

In Newtonian mechanics, the relative velocity is independent of the chosen inertial reference frame. This is not the case anymore with special relativity in which velocities depend on the choice of reference frame.

If an object A is moving with velocity vector v and an object B with velocity vector w , then the velocity of object A relative to object B is defined as the difference of the two velocity vectors:.

Similarly, the relative velocity of object B moving with velocity w , relative to object A moving with velocity v is:.

Usually, the inertial frame chosen is that in which the latter of the two mentioned objects is in rest. In the one-dimensional case, [3] the velocities are scalars and the equation is either:.

In polar coordinates , a two-dimensional velocity is described by a radial velocity , defined as the component of velocity away from or toward the origin also known as velocity made good , and an angular velocity , which is the rate of rotation about the origin with positive quantities representing counter-clockwise rotation and negative quantities representing clockwise rotation, in a right-handed coordinate system.

The radial and angular velocities can be derived from the Cartesian velocity and displacement vectors by decomposing the velocity vector into radial and transverse components.

The transverse velocity is the component of velocity along a circle centered at the origin. The magnitude of the radial velocity is the dot product of the velocity vector and the unit vector in the direction of the displacement.

The magnitude of the transverse velocity is that of the cross product of the unit vector in the direction of the displacement and the velocity vector.

Angular momentum in scalar form is the mass times the distance to the origin times the transverse velocity, or equivalently, the mass times the distance squared times the angular speed.

The sign convention for angular momentum is the same as that for angular velocity. Section Navigation. How von Willebrand Disease is Inherited.

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