From Wikipedia, the free encyclopedia Velocity
Velocity
Classical mechanics In physics, velocity is speed in a given direction. Speed
describes only how fast an object is moving, whereas ve-
locity gives both the speed and direction of the object’s
Newton’s Second Law motion. To have a constant velocity, an object must have
History of classical mechanics · Timeline of classical a constant speed and motion in a constant direction. Con-
mechanics stant direction typically constrains the object to motion
in a straight path. A car moving at a constant 20 kilo-
Branches meters per hour in a circular path does not have a con-
Statics · Dynamics / Kinetics · Kinematics · Applied stant velocity. The rate of change in velocity is acceler-
mechanics · Celestial mechanics · Continuum me- ation. Velocity is a vector physical quantity; both mag-
chanics · Statistical mechanics nitude and direction are required to define it. The scalar
Formulations absolute value (magnitude) of velocity is speed, a quan-
• Newtonian mechanics (Vectorial mechanics) tity that is measured in metres per second (m/s or ms−1)
• Analytical mechanics: when using the SI (metric) system.
• Lagrangian mechanics For example, "5 metres per second" is a scalar and not
• Hamiltonian mechanics a vector, whereas "5 metres per second east" is a vector.
The average velocity v of an object moving through a dis-
Fundamental concepts
Space · Time · Velocity · Speed · Mass · Acceleration · placement during a time interval (Δt) is described
Gravity · Force · Impulse · Torque / Moment / Couple · by the formula:
Momentum · Angular momentum · Inertia · Moment
of inertia · Reference frame · Energy · Kinetic energy ·
Potential energy · Mechanical work · Virtual work ·
D’Alembert’s principle The rate of change of velocity (in m/s) as a function of
Core topics time (in s) is acceleration (in m/s²) – how an object’s
Rigid body · Rigid body dynamics · Euler’s equations speed or direction of travel changes over time, and how
(rigid body dynamics) · Motion · Newton’s laws of mo- it is changing at a particular point in time.
tion · Newton’s law of universal gravitation · Euler’s
laws of motion · Equations of motion · Inertial frame Equation of motion
of reference · Non-inertial reference frame · Rotating
reference frame · Fictitious force · Linear motion · Me- Main article: Equation of motion
chanics of planar particle motion · Displacement The velocity vector v of an object that has positions x(t)
(vector) · Relative velocity · Friction · Simple harmon- at time t and x(t + Δt) at time t + Δt, can be computed as
ic motion · Harmonic oscillator · Vibration · Damping · the derivative of position:
Damping ratio · Rotational motion · Circular motion ·
Uniform circular motion · Non-uniform circular mo-
tion · Centripetal force · Centrifugal force · Centrifugal
force (rotating reference frame) · Reactive centrifugal Average velocity magnitudes always smaller than or
force · Coriolis force · Pendulum · Rotational speed · equal to average speed of a given particle. Instantaneous
Angular acceleration · Angular velocity · Angular fre- velocity is always tangential to trajectory. Slope of tan-
quency · Angular displacement gent of position or displacement time graph is instanta-
Scientists neous velocity and its slope of chord is average velocity.
Galileo Galilei · Isaac Newton · Jeremiah Horrocks · The equation for an object’s velocity can be obtained
Leonhard Euler · Jean le Rond d’Alembert · Alexis mathematically by evaluating the integral of the equa-
Clairaut · Joseph Louis Lagrange · Pierre-Simon tion for its acceleration beginning from some initial peri-
Laplace · William Rowan Hamilton · Siméon-Denis od time t0 to some point in time later tn.
Poisson The final velocity v of an object which starts with ve-
locity u and then accelerates at constant acceleration a
for a period of time Δt is:
1
From Wikipedia, the free encyclopedia Velocity
Relative velocity is fundamental in both classical and
modern physics, since many systems in physics deal with
The average velocity of an object undergoing constant the relative motion of two or more particles. In Newton-
ian mechanics, the relative velocity is independent of the
acceleration is , where u is the initial velocity and chosen inertial reference frame. This is not the case any-
v is the final velocity. To find the position, x, of such an more with special relativity in which velocities depend
accelerating object during a time interval, Δt, then: 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 ob-
ject A relative to object B is defined as the difference of the
two velocity vectors:
When only the object’s initial velocity is known, the ex-
pression,
Similarly the relative velocity of object B moving with ve-
locity w, relative to object A moving with velocity v is:
can be used.
This can be expanded to give the position at any time Usually the inertial frame is chosen in which the latter of
t in the following way: the two mentioned objects is in rest.
Scalar velocities
In the one dimensional case,[1] the velocities are scalars
These basic equations for final velocity and position can and the equation is either:
be combined to form an equation that is independent of
time, also known as Torricelli’s equation: , if the two objects are
moving in opposite directions, or:
The above equations are valid for both Newtonian me- , if the two objects are
chanics and special relativity. Where Newtonian me- moving in the same direction.
chanics and special relativity differ is in how different
observers would describe the same situation. In particu- Polar coordinates
lar, in Newtonian mechanics, all observers agree on the
value of t and the transformation rules for position create In polar coordinates, a two-dimensional velocity is de-
a situation in which all non-accelerating observers would scribed by a radial velocity, defined as the component
describe the acceleration of an object with the same val- of velocity away from or toward the origin (also known
ues. Neither is true for special relativity. In other words as velocity made good), and an angular velocity, which is
only relative velocity can be calculated. the rate of rotation about the origin (with positive quan-
In Newtonian mechanics, the kinetic energy (energy tities representing counter-clockwise rotation and neg-
of motion), EK, of a moving object is linear with both its ative quantities representing clockwise rotation, in a
mass and the square of its velocity: right-handed coordinate system).
The radial and angular velocities can be derived from
the Cartesian velocity and displacement vectors by de-
composing the velocity vector into radial and transverse
The kinetic energy is a scalar quantity. components. The transverse velocity is the component of
Escape velocity is the minimum velocity a body must velocity along a circle centered at the origin.
have in order to escape from the gravitational field of the
earth. To escape from the Earth’s gravitational field an
object must have greater kinetic energy than its gravita- where
tional potential energy. The value of the escape velocity is the transverse velocity
from the Earth’s surface is approximately 11100 m/s.
is the radial velocity.
Relative velocity The magnitude of the radial velocity is the dot product of
Main article: Relative velocity the velocity vector and the unit vector in the direction of
Relative velocity is a measurement of velocity between the displacement.
two objects as determined in a single coordinate system.
2
From Wikipedia, the free encyclopedia Velocity
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 rela-
where
tions are known as Kepler’s laws of planetary motion.
is displacement.
The magnitude of the transverse velocity is that of the cross See also
product of the unit vector in the direction of the dis-
placement and the velocity vector. It is also the product • Escape velocity
of the angular speed ω and the magnitude of the dis- • Four-velocity (relativistic version of velocity for
placement. Minkowski spacetime)
• Group velocity
• Hypervelocity
• Kinematics
• Phase velocity
such that • Proper velocity (in relativity, using traveler time
instead of observer time)
• Rapidity (a version of velocity additive at relativistic
speeds)
• Relative velocity
Angular momentum in scalar form is the mass times the • Terminal velocity
distance to the origin times the transverse velocity, or • Velocity vs. time graph
equivalently, the mass times the distance squared times
the angular speed. The sign convention for angular mo-
mentum is the same as that for angular velocity. References
[1] Basic principle
• Robert Resnick and Jearl Walker, Fundamentals of
where Physics, Wiley; 7 Sub edition (June 16, 2004). ISBN
is mass 0471232319.
External links
The expression mr2 is known as moment of inertia. If • Physicsclassroom.com, Speed and Velocity
forces are in the radial direction only with an inverse • Introduction to Mechanisms (Carnegie Mellon
square dependence, as in the case of a gravitational orbit, University)
Retrieved from "http://en.wikipedia.org/w/index.php?title=Velocity&oldid=474026212"
Categories:
• Motion
• Kinematics
• Velocity
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