BikeParts Wiki


474pages on
this wiki
Add New Page
Talk0 Share
Classical mechanics
History of ...
Fundamental concepts
Space · Time · Velocity · Speed · Mass · Acceleration · Gravity · Force · Impulse · Torque / Moment / Couple · Momentum · Angular momentum · Inertia · Moment of inertia · Reference frame · Energy · Kinetic energy · Potential energy · Mechanical work · Virtual work · D'Alembert's principle
For the waltz composed by Johann Strauss, see Accelerationen.
File:Acceleration components.JPG

In physics, and more specifically kinematics, acceleration is the change in velocity over time.[1] Because velocity is a vector, it can change in two ways: a change in magnitude and/or a change in direction. In one dimension, i.e. a line, acceleration is the rate at which something speeds up or slows down. However, as a vector quantity, acceleration is also the rate at which direction changes.[2][3] Acceleration has the dimensions L T−2. In SI units, acceleration is measured in metres per second squared (m/s2).

In common speech, the term acceleration commonly is used for an increase in speed (the magnitude of velocity); a decrease in speed is called deceleration. In physics, a change in the direction of velocity also is an acceleration: for rotary motion, the change in direction of velocity results in centripetal (toward the center) acceleration; where as the rate of change of speed is a tangential acceleration.

In classical mechanics, for a body with constant mass, the acceleration of the body is proportional to the resultant (total) force acting on it (Newton's second law):

\mathbf{F} = m\mathbf{a} \quad \to \quad \mathbf{a} = \mathbf{F}/m

where F is the resultant force acting on the body, m is the mass of the body, and a is its acceleration.

Average and instantaneous accelerationEdit

Average acceleration is the change in velocity (Δv) divided by the change in time (Δt). Instantaneous acceleration is the acceleration at a specific point in time which is for a very short interval of time as Δt approaches zero.

Tangential and centripetal accelerationEdit

The velocity of a particle moving on a curved path as a function of time can be written as:

\mathbf{v} (t) =v(t) \frac {\mathbf{v}(t)}{v(t)} = v(t) \mathbf{u}_\mathrm{t}(t) ,

with v(t) equal to the speed of travel along the path, and

\mathbf{u}_\mathrm{t} = \frac {\mathbf{v}(t)}{v(t)} \ ,

a unit vector tangent to the path pointing in the direction of motion at the chosen moment in time. Taking into account both the changing speed v(t) and the changing direction of ut, the acceleration of a particle moving on a curved path on a planar surface can be written using the chain rule of differentiation as:

\mathbf{a} & = \frac{d \mathbf{v}}{dt} \\
           & =  \frac{\mathrm{d}v }{\mathrm{d}t} \mathbf{u}_\mathrm{t} +v(t)\frac{d \mathbf{u}_\mathrm{t}}{dt} \\
           & = \frac{\mathrm{d}v }{\mathrm{d}t} \mathbf{u}_\mathrm{t}+ \frac{v^2}{R}\mathbf{u}_\mathrm{n}\ , \\

where un is the unit (outward) normal vector to the particle's trajectory, and R is its instantaneous radius of curvature based upon the osculating circle at time t. These components are called the tangential acceleration and the radial acceleration, respectively. The negative of the radial acceleration is the centripetal acceleration, which points inward, toward the center of curvature.

Extension of this approach to three-dimensional space curves that cannot be contained on a planar surface leads to the Frenet-Serret formulas.[4][5]

Relation to relativityEdit

After completing his theory of special relativity, Albert Einstein realized that forces felt by objects undergoing constant proper acceleration are actually feeling themselves being accelerated, so that, for example, a car's acceleration forwards would result in the driver feeling a slight pressure between himself and his seat. In the case of gravity, which Einstein concluded is not actually a force, this is not the case; acceleration due to gravity is not felt by an object in free-fall. This was the basis for his development of general relativity, a relativistic theory of gravity.

Notes Edit

  1. Crew, Henry (2008). The Principles of Mechanics. BiblioBazaar, LLC. pp. 43. ISBN 0559368712. 
  2. Bondi, Hermann (1980). Relativity and Common Sense. Courier Dover Publications. pp. 3. ISBN 0486240215. 
  3. Lehrman, Robert L. (1998). Physics the Easy Way. Barron's Educational Series. pp. 27. ISBN 0764102362. 
  4. Larry C. Andrews & Ronald L. Phillips (2003). Mathematical Techniques for Engineers and Scientists. SPIE Press. p. 164. ISBN 0819445061.,M1. 
  5. Ch V Ramana Murthy & NC Srinivas (2001). Applied Mathematics. New Delhi: S. Chand & Co.. p. 337. ISBN 81-219-2082-5. 

See also Edit

External linksEdit


ar:تسارع an:Aceleración ast:Aceleración az:Təcil bn:ত্বরণ zh-min-nan:Ka-sok-tō͘ be:Паскарэнне be-x-old:Паскарэньне bs:Ubrzanje bg:Ускорение ca:Acceleració cs:Zrychlení cy:Cyflymiad da:Acceleration de:Beschleunigung et:Kiirendus el:Επιτάχυνση es:Aceleración eo:Akcelo eu:Azelerazio fa:شتاب fr:Accélération ga:Luasghéarú gv:Bieauaghey gl:Aceleración hak:Kâ-suk-thu ko:가속도 hr:Ubrzanje io:Acelero id:Percepatan ia:Acceleration is:Hröðun it:Accelerazione he:תאוצה krc:Терклениу ka:აჩქარება la:Acceleratio lv:Paātrinājums lt:Pagreitis hu:Gyorsulás ml:ത്വരണം arz:عجله ms:Pecutan mn:Хурдатгал nl:Versnelling (natuurkunde) ja:加速度 no:Akselerasjon nn:Akselerasjon nov:Akseleratione pnb:اسراع km:សំទុះ pl:Przyspieszenie pt:Aceleração ro:Acceleraţie liniară qu:P'ikwachiy ru:Ускорение sq:Nxitimi scn:Accilirazzioni simple:Acceleration sk:Zrýchlenie sl:Pospešek szl:Szwůng ckb:لەز sr:Убрзање sh:Ubrzanje su:Akselerasi fi:Kiihtyvyys sv:Acceleration ta:முடுக்கம் te:త్వరణము th:ความเร่ง tr:İvme uk:Прискорення ur:اسراع vi:Gia tốc fiu-vro:Kipõndus war:Akselerasyon yi:פארגיכערונג zh-yue:加速度 zh:加速度

Ad blocker interference detected!

Wikia is a free-to-use site that makes money from advertising. We have a modified experience for viewers using ad blockers

Wikia is not accessible if you’ve made further modifications. Remove the custom ad blocker rule(s) and the page will load as expected.