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Velocity is the directional speed of a object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g.60 km/h northbound). Velocity is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of bodies.

Velocity
As a change of direction occurs while the racing cars turn on the curved track, their velocity is not constant.
Common symbols
v,v,v
Other units
mph, ft/s
In SI base unitsm/s
DimensionL T−1

Velocity is a physical vector quantity; both magnitude and direction are needed to define it. The scalar absolute value (magnitude) of velocity is called speed, being a coherent derived unit whose quantity is measured in the SI (metric system) as metres per second (m/s or m⋅s−1). For example, "5 metres per second" is a scalar, whereas "5 metres per second east" is a vector. If there is a change in speed, direction or both, then the object is said to be undergoing an acceleration.

Contents

To have a constant velocity, an object must have a constant speed in a constant direction. Constant direction constrains the object to motion in a straight path thus, a constant velocity means motion in a straight line at a constant speed.

For example, a car moving at a constant 20 kilometres per hour in a circular path has a constant speed, but does not have a constant velocity because its direction changes. Hence, the car is considered to be undergoing an acceleration.

Main article: Speed
Kinematic quantities of a classical particle: mass m, position r, velocity v, acceleration a.

Speed, the scalar magnitude of a velocity vector, denotes only how fast an object is moving.

Main article: Equation of motion

Average velocity

Velocity is defined as the rate of change of position with respect to time, which may also be referred to as the instantaneous velocity to emphasize the distinction from the average velocity. In some applications the average velocity of an object might be needed, that is to say, the constant velocity that would provide the same resultant displacement as a variable velocity in the same time interval,v(t), over some time periodΔt. Average velocity can be calculated as:

v ¯ = Δ x Δ t . {\displaystyle {\boldsymbol {\bar {v}}}={\frac {\Delta {\boldsymbol {x}}}{\Delta t}}.}

The average velocity is always less than or equal to the average speed of an object. This can be seen by realizing that while distance is always strictly increasing, displacement can increase or decrease in magnitude as well as change direction.

In terms of a displacement-time (x vs. t) graph, the instantaneous velocity (or, simply, velocity) can be thought of as the slope of the tangent line to the curve at any point, and the average velocity as the slope of the secant line between two points with t coordinates equal to the boundaries of the time period for the average velocity.

The average velocity is the same as the velocity averaged over time – that is to say, its time-weighted average, which may be calculated as the time integral of the velocity:

v ¯ = 1 t 1 t 0 t 0 t 1 v ( t ) d t , {\displaystyle {\boldsymbol {\bar {v}}}={1 \over t_{1}-t_{0}}\int _{t_{0}}^{t_{1}}{\boldsymbol {v}}(t)\ dt,}

where we may identify

Δ x = t 0 t 1 v ( t ) d t {\displaystyle \Delta {\boldsymbol {x}}=\int _{t_{0}}^{t_{1}}{\boldsymbol {v}}(t)\ dt}

and

Δ t = t 1 t 0 . {\displaystyle \Delta t=t_{1}-t_{0}.}

Instantaneous velocity

Example of a velocity vs. time graph, and the relationship between velocity v on the y-axis, acceleration a (the three green tangent lines represent the values for acceleration at different points along the curve) and displacement s (the yellow area under the curve.)

If we considerv as velocity andx as the displacement (change in position) vector, then we can express the (instantaneous) velocity of a particle or object, at any particular timet, as the derivative of the position with respect to time:

v = lim Δ t 0 Δ x Δ t = d x d t . {\displaystyle {\boldsymbol {v}}=\lim _{{\Delta t}\to 0}{\frac {\Delta {\boldsymbol {x}}}{\Delta t}}={\frac {d{\boldsymbol {x}}}{dt}}.}

From this derivative equation, in the one-dimensional case it can be seen that the area under a velocity vs. time (v vs.t graph) is the displacement,x. In calculus terms, the integral of the velocity functionv(t) is the displacement functionx(t). In the figure, this corresponds to the yellow area under the curve labeleds (s being an alternative notation for displacement).

x = v d t . {\displaystyle {\boldsymbol {x}}=\int {\boldsymbol {v}}\ dt.}

Since the derivative of the position with respect to time gives the change in position (in metres) divided by the change in time (in seconds), velocity is measured in metres per second (m/s). Although the concept of an instantaneous velocity might at first seem counter-intuitive, it may be thought of as the velocity that the object would continue to travel at if it stopped accelerating at that moment.

Relationship to acceleration

Although velocity is defined as the rate of change of position, it is often common to start with an expression for an object's acceleration. As seen by the three green tangent lines in the figure, an object's instantaneous acceleration at a point in time is the slope of the line tangent to the curve of av(t) graph at that point. In other words, acceleration is defined as the derivative of velocity with respect to time:

a = d v d t . {\displaystyle {\boldsymbol {a}}={\frac {d{\boldsymbol {v}}}{dt}}.}

From there, we can obtain an expression for velocity as the area under ana(t) acceleration vs. time graph. As above, this is done using the concept of the integral:

v = a d t . {\displaystyle {\boldsymbol {v}}=\int {\boldsymbol {a}}\ dt.}

Constant acceleration

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

v = u + a t {\displaystyle {\boldsymbol {v}}={\boldsymbol {u}}+{\boldsymbol {a}}t}

withv as the velocity at timet andu as the velocity at timet = 0. By combining this equation with the suvat equationx = ut + at2/2, it is possible to relate the displacement and the average velocity by

x = ( u + v ) 2 t = v ¯ t . {\displaystyle {\boldsymbol {x}}={\frac {({\boldsymbol {u}}+{\boldsymbol {v}})}{2}}t={\boldsymbol {\bar {v}}}t.}

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

v 2 = v v = ( u + a t ) ( u + a t ) = u 2 + 2 t ( a u ) + a 2 t 2 {\displaystyle v^{2}={\boldsymbol {v}}\cdot {\boldsymbol {v}}=({\boldsymbol {u}}+{\boldsymbol {a}}t)\cdot ({\boldsymbol {u}}+{\boldsymbol {a}}t)=u^{2}+2t({\boldsymbol {a}}\cdot {\boldsymbol {u}})+a^{2}t^{2}}
( 2 a ) x = ( 2 a ) ( u t + 1 2 a t 2 ) = 2 t ( a u ) + a 2 t 2 = v 2 u 2 {\displaystyle (2{\boldsymbol {a}})\cdot {\boldsymbol {x}}=(2{\boldsymbol {a}})\cdot ({\boldsymbol {u}}t+{\tfrac {1}{2}}{\boldsymbol {a}}t^{2})=2t({\boldsymbol {a}}\cdot {\boldsymbol {u}})+a^{2}t^{2}=v^{2}-u^{2}}
v 2 = u 2 + 2 ( a x ) {\displaystyle \therefore v^{2}=u^{2}+2({\boldsymbol {a}}\cdot {\boldsymbol {x}})}

wherev = |v| etc.

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.

Quantities that are dependent on velocity

The kinetic energy of a moving object is dependent on its velocity and is given by the equation

E k = 1 2 m v 2 {\displaystyle E_{\text{k}}={\tfrac {1}{2}}mv^{2}}

ignoring special relativity, where Ek is the kinetic energy and m is the mass. 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

p = m v {\displaystyle {\boldsymbol {p}}=m{\boldsymbol {v}}}

In special relativity, the dimensionless Lorentz factor appears frequently, and is given by

γ = 1 1 v 2 c 2 {\displaystyle \gamma ={\frac {1}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}}

where γ is the Lorentz factor and c is the speed of light.

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

v e = 2 G M r = 2 g r , {\displaystyle v_{\text{e}}={\sqrt {\frac {2GM}{r}}}={\sqrt {2gr}},}

where G is the gravitational constant and g is the gravitational acceleration. The escape velocity from Earth's surface is about 11 200 m/s, and is irrespective of the direction of the object. 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.

Main article: Relative velocity

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:

v A relative to B = v w {\displaystyle {\boldsymbol {v}}_{A{\text{ relative to }}B}={\boldsymbol {v}}-{\boldsymbol {w}}}

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

v B relative to A = w v {\displaystyle {\boldsymbol {v}}_{B{\text{ relative to }}A}={\boldsymbol {w}}-{\boldsymbol {v}}}

Usually, the inertial frame chosen is that in which the latter of the two mentioned objects is in rest.

Scalar velocities

In the one-dimensional case, the velocities are scalars and the equation is either:

v rel = v ( w ) {\displaystyle v_{\text{rel}}=v-(-w)} , if the two objects are moving in opposite directions, or:
v rel = v ( + w ) {\displaystyle v_{\text{rel}}=v-(+w)} , if the two objects are moving in the same direction.
Representation of radial and tangential components of velocity at different moments of linear motion with constant velocity of the object around an observer O (it corresponds, for example, to the passage of a car on a straight street around a pedestrian standing on the sidewalk). The radial component can be observed due to the Doppler effect, the tangential component causes visible changes of the position of the object.

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.

v = v T + v R {\displaystyle {\boldsymbol {v}}={\boldsymbol {v}}_{T}+{\boldsymbol {v}}_{R}}

where

  • v T {\displaystyle {\boldsymbol {v}}_{T}} is the transverse velocity
  • v R {\displaystyle {\boldsymbol {v}}_{R}} is the radial velocity.

The magnitude of the radial velocity is the dot product of the velocity vector and the unit vector in the direction of the displacement.

v R = v r | r | {\displaystyle v_{R}={\frac {{\boldsymbol {v}}\cdot {\boldsymbol {r}}}{\left|{\boldsymbol {r}}\right|}}}

where r {\displaystyle {\boldsymbol {r}}} is 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. It is also the product of the angular speed ω {\displaystyle \omega } and the magnitude of the displacement.

v T = | r × v | | r | = ω | r | {\displaystyle v_{T}={\frac {|{\boldsymbol {r}}\times {\boldsymbol {v}}|}{|{\boldsymbol {r}}|}}=\omega |{\boldsymbol {r}}|}

such that

ω = | r × v | | r | 2 . {\displaystyle \omega ={\frac {|{\boldsymbol {r}}\times {\boldsymbol {v}}|}{|{\boldsymbol {r}}|^{2}}}.}

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.

L = m r v T = m r 2 ω {\displaystyle L=mrv_{T}=mr^{2}\omega }

where

  • m {\displaystyle m} is mass
  • r = | r | . {\displaystyle r=|{\boldsymbol {r}}|.}

The expression m r 2 {\displaystyle mr^{2}} is known as moment of inertia. 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.

  1. "velocity". Lexico dictionary. 2022. Retrieved2 May 2022.
  2. Rowland, Todd (2019). "Velocity Vector". Wolfram MathWorld. Retrieved2 June 2019.
  3. Wilson, Edwin Bidwell (1901). Vector analysis: a text-book for the use of students of mathematics and physics, founded upon the lectures of J. Willard Gibbs. Yale bicentennial publications. C. Scribner's Sons. p. 125. hdl:2027/mdp.39015000962285. Earliest occurrence of the speed/velocity terminology.
  4. Basic principle
  • Robert Resnick and Jearl Walker, Fundamentals of Physics, Wiley; 7 Sub edition (June 16, 2004). ISBN 0-471-23231-9.
Wikimedia Commons has media related toVelocity.

Velocity Article Talk Language Watch Edit This article is about velocity in physics For other uses see Velocity disambiguation 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 Find sources Velocity news newspapers books scholar JSTOR March 2011 Learn how and when to remove this template message Velocity is the directional speed of a object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time e g 60 km h northbound 1 Velocity is a fundamental concept in kinematics the branch of classical mechanics that describes the motion of bodies VelocityAs a change of direction occurs while the racing cars turn on the curved track their velocity is not constant Common symbolsv v v Other unitsmph ft sIn SI base unitsm sDimensionL T 1 Velocity is a physical vector quantity both magnitude and direction are needed to define it The scalar absolute value magnitude of velocity is called speed being a coherent derived unit whose quantity is measured in the SI metric system as metres per second m s or m s 1 For example 5 metres per second is a scalar whereas 5 metres per second east is a vector If there is a change in speed direction or both then the object is said to be undergoing an acceleration Contents 1 Constant velocity vs acceleration 2 Difference between speed and velocity 3 Equation of motion 3 1 Average velocity 3 2 Instantaneous velocity 3 3 Relationship to acceleration 3 3 1 Constant acceleration 3 4 Quantities that are dependent on velocity 4 Relative velocity 4 1 Scalar velocities 5 Polar coordinates 6 See also 7 Notes 8 References 9 External linksConstant velocity vs accelerationTo have a constant velocity an object must have a constant speed in a constant direction Constant direction constrains the object to motion in a straight path thus a constant velocity means motion in a straight line at a constant speed For example a car moving at a constant 20 kilometres per hour in a circular path has a constant speed but does not have a constant velocity because its direction changes Hence the car is considered to be undergoing an acceleration Difference between speed and velocityMain article Speed Kinematic quantities of a classical particle mass m position r velocity v acceleration a Speed the scalar magnitude of a velocity vector denotes only how fast an object is moving 2 3 Equation of motionMain article Equation of motion Average velocity Velocity is defined as the rate of change of position with respect to time which may also be referred to as the instantaneous velocity to emphasize the distinction from the average velocity In some applications the average velocity of an object might be needed that is to say the constant velocity that would provide the same resultant displacement as a variable velocity in the same time interval v t over some time period Dt Average velocity can be calculated as v D x D t displaystyle boldsymbol bar v frac Delta boldsymbol x Delta t The average velocity is always less than or equal to the average speed of an object This can be seen by realizing that while distance is always strictly increasing displacement can increase or decrease in magnitude as well as change direction In terms of a displacement time x vs t graph the instantaneous velocity or simply velocity can be thought of as the slope of the tangent line to the curve at any point and the average velocity as the slope of the secant line between two points with t coordinates equal to the boundaries of the time period for the average velocity The average velocity is the same as the velocity averaged over time that is to say its time weighted average which may be calculated as the time integral of the velocity v 1 t 1 t 0 t 0 t 1 v t d t displaystyle boldsymbol bar v 1 over t 1 t 0 int t 0 t 1 boldsymbol v t dt where we may identify D x t 0 t 1 v t d t displaystyle Delta boldsymbol x int t 0 t 1 boldsymbol v t dt and D t t 1 t 0 displaystyle Delta t t 1 t 0 Instantaneous velocity Example of a velocity vs time graph and the relationship between velocity v on the y axis acceleration a the three green tangent lines represent the values for acceleration at different points along the curve and displacement s the yellow area under the curve If we consider v as velocity and x as the displacement change in position vector then we can express the instantaneous velocity of a particle or object at any particular time t as the derivative of the position with respect to time v lim D t 0 D x D t d x d t displaystyle boldsymbol v lim Delta t to 0 frac Delta boldsymbol x Delta t frac d boldsymbol x dt From this derivative equation in the one dimensional case it can be seen that the area under a velocity vs time v vs t graph is the displacement x In calculus terms the integral of the velocity function v t is the displacement function x t In the figure this corresponds to the yellow area under the curve labeled s s being an alternative notation for displacement x v d t displaystyle boldsymbol x int boldsymbol v dt Since the derivative of the position with respect to time gives the change in position in metres divided by the change in time in seconds velocity is measured in metres per second m s Although the concept of an instantaneous velocity might at first seem counter intuitive it may be thought of as the velocity that the object would continue to travel at if it stopped accelerating at that moment Relationship to acceleration Although velocity is defined as the rate of change of position it is often common to start with an expression for an object s acceleration As seen by the three green tangent lines in the figure an object s instantaneous acceleration at a point in time is the slope of the line tangent to the curve of a v t graph at that point In other words acceleration is defined as the derivative of velocity with respect to time a d v d t displaystyle boldsymbol a frac d boldsymbol v dt From there we can obtain an expression for velocity as the area under an a t acceleration vs time graph As above this is done using the concept of the integral v a d t displaystyle boldsymbol v int boldsymbol a dt Constant acceleration 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 v u a t displaystyle boldsymbol v boldsymbol u boldsymbol a t with v as the velocity at time t and u as the velocity at time t 0 By combining this equation with the suvat equation x ut at2 2 it is possible to relate the displacement and the average velocity by x u v 2 t v t displaystyle boldsymbol x frac boldsymbol u boldsymbol v 2 t boldsymbol bar v t It is also possible to derive an expression for the velocity independent of time known as the Torricelli equation as follows v 2 v v u a t u a t u 2 2 t a u a 2 t 2 displaystyle v 2 boldsymbol v cdot boldsymbol v boldsymbol u boldsymbol a t cdot boldsymbol u boldsymbol a t u 2 2t boldsymbol a cdot boldsymbol u a 2 t 2 2 a x 2 a u t 1 2 a t 2 2 t a u a 2 t 2 v 2 u 2 displaystyle 2 boldsymbol a cdot boldsymbol x 2 boldsymbol a cdot boldsymbol u t tfrac 1 2 boldsymbol a t 2 2t boldsymbol a cdot boldsymbol u a 2 t 2 v 2 u 2 v 2 u 2 2 a x displaystyle therefore v 2 u 2 2 boldsymbol a cdot boldsymbol x where v v etc 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 Quantities that are dependent on velocity The kinetic energy of a moving object is dependent on its velocity and is given by the equation E k 1 2 m v 2 displaystyle E text k tfrac 1 2 mv 2 ignoring special relativity where Ek is the kinetic energy and m is the mass 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 p m v displaystyle boldsymbol p m boldsymbol v In special relativity the dimensionless Lorentz factor appears frequently and is given by g 1 1 v 2 c 2 displaystyle gamma frac 1 sqrt 1 frac v 2 c 2 where g is the Lorentz factor and c is the speed of light 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 v e 2 G M r 2 g r displaystyle v text e sqrt frac 2GM r sqrt 2gr where G is the gravitational constant and g is the gravitational acceleration The escape velocity from Earth s surface is about 11 200 m s and is irrespective of the direction of the object 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 velocityMain article Relative velocity 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 v A relative to B v w displaystyle boldsymbol v A text relative to B boldsymbol v boldsymbol w Similarly the relative velocity of object B moving with velocity w relative to object A moving with velocity v is v B relative to A w v displaystyle boldsymbol v B text relative to A boldsymbol w boldsymbol v Usually the inertial frame chosen is that in which the latter of the two mentioned objects is in rest Scalar velocities In the one dimensional case 4 the velocities are scalars and the equation is either v rel v w displaystyle v text rel v w if the two objects are moving in opposite directions or v rel v w displaystyle v text rel v w if the two objects are moving in the same direction Polar coordinates Representation of radial and tangential components of velocity at different moments of linear motion with constant velocity of the object around an observer O it corresponds for example to the passage of a car on a straight street around a pedestrian standing on the sidewalk The radial component can be observed due to the Doppler effect the tangential component causes visible changes of the position of the object 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 v v T v R displaystyle boldsymbol v boldsymbol v T boldsymbol v R where v T displaystyle boldsymbol v T is the transverse velocity v R displaystyle boldsymbol v R is the radial velocity The magnitude of the radial velocity is the dot product of the velocity vector and the unit vector in the direction of the displacement v R v r r displaystyle v R frac boldsymbol v cdot boldsymbol r left boldsymbol r right where r displaystyle boldsymbol r is 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 It is also the product of the angular speed w displaystyle omega and the magnitude of the displacement v T r v r w r displaystyle v T frac boldsymbol r times boldsymbol v boldsymbol r omega boldsymbol r such that w r v r 2 displaystyle omega frac boldsymbol r times boldsymbol v boldsymbol r 2 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 L m r v T m r 2 w displaystyle L mrv T mr 2 omega where m displaystyle m is mass r r displaystyle r boldsymbol r The expression m r 2 displaystyle mr 2 is known as moment of inertia 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 See alsoFour 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 time graphNotes velocity Lexico dictionary 2022 Retrieved 2 May 2022 Rowland Todd 2019 Velocity Vector Wolfram MathWorld Retrieved 2 June 2019 Wilson Edwin Bidwell 1901 Vector analysis a text book for the use of students of mathematics and physics founded upon the lectures of J Willard Gibbs Yale bicentennial publications C Scribner s Sons p 125 hdl 2027 mdp 39015000962285 Earliest occurrence of the speed velocity terminology Basic principleReferencesRobert Resnick and Jearl Walker Fundamentals of Physics Wiley 7 Sub edition June 16 2004 ISBN 0 471 23231 9 External linksWikimedia Commons has media related to Velocity Velocity and Acceleration Introduction to Mechanisms Carnegie Mellon University Retrieved from https en wikipedia org w index php title Velocity amp oldid 1090317737, wikipedia, wiki, book,

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