Centripetalna sila — разлика између измена
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{{Short description|Sila usmerena ka centru rotacije}} |
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[[Датотека:Centripetal acceleration.JPG|мини|Na telo koje se kreće po kružnici deluje centripetalna sila koja je usmerena duž poluprečnika kruga tački na kružnici u kojoj se telo u tom trenutku nalazi ka centru kružnice.]] |
[[Датотека:Centripetal acceleration.JPG|мини|Na telo koje se kreće po kružnici deluje centripetalna sila koja je usmerena duž poluprečnika kruga tački na kružnici u kojoj se telo u tom trenutku nalazi ka centru kružnice.]] |
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'''Centripetalna sila''' (od [[Латински језик|latinskih reči]] -{''centrum''}-, „centar” i -{''petere''}-, „tražiti”<ref>{{cite book |title=A new universal etymological, technological and pronouncing dictionary of the English language: embracing all terms used in art, science, and literature, Volume 1 |first1=John |last1=Craig |publisher=Harvard University |year=1849 |page=291 |url=https://books.google.com/books?id=0nxBAAAAYAAJ}} [https://books.google.com/books?id=0nxBAAAAYAAJ&pg=PA291 Extract of page 291]</ref>) je [[sila]] koja uzrokuje da telo sledi zakrivljenu putanju. Njen pravac je uvek [[Ортогоналност|ortogonalan]] na vektor brzine tela u datoj tački i usmeren je prema centru zakrivljenosti putanje. |
'''Centripetalna sila''' (od [[Латински језик|latinskih reči]] -{''centrum''}-, „centar” i -{''petere''}-, „tražiti”<ref>{{cite book |title=A new universal etymological, technological and pronouncing dictionary of the English language: embracing all terms used in art, science, and literature, Volume 1 |first1=John |last1=Craig |publisher=Harvard University |year=1849 |page=291 |url=https://books.google.com/books?id=0nxBAAAAYAAJ}} [https://books.google.com/books?id=0nxBAAAAYAAJ&pg=PA291 Extract of page 291]</ref>) je [[sila]] koja uzrokuje da telo sledi zakrivljenu putanju. Njen pravac je uvek [[Ортогоналност|ortogonalan]] na vektor brzine tela u datoj tački i usmeren je prema centru zakrivljenosti putanje. |
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== Formula == |
== Formula == |
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Centripetalna sila koja deluje na objekt mase -{''m''}- koji se kreće po kružnici je zadata [[Њутнови закони|Drugim Njutnovim zakonom]]: |
Centripetalna sila koja deluje na objekt mase -{''m''}- koji se kreće po kružnici je zadata [[Њутнови закони|Drugim Njutnovim zakonom]]: |
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gde je <math>a_c</math> [[Убрзање|centripetalno ubrzanje]] koje se za telo koje se kreće [[Брзина|tangencijalnom brzinom]] -{''v''}- duž puta [[Пречник|radijusa zakrivljenosti]] -{''r''}- može izračunati kao:<ref>{{cite book|title=Facts and Practice for A-Level: Physics|author=Chris Carter|publisher=Oxford University Press|year=2001|isbn=978-0-19-914768-7|location=S.2.|page=30}}</ref> |
gde je <math>a_c</math> [[Убрзање|centripetalno ubrzanje]] koje se za telo koje se kreće [[Брзина|tangencijalnom brzinom]] -{''v''}- duž puta [[Пречник|radijusa zakrivljenosti]] -{''r''}- može izračunati kao:<ref>{{cite book|title=Facts and Practice for A-Level: Physics|author=Chris Carter|publisher=Oxford University Press|year=2001|isbn=978-0-19-914768-7|location=S.2.|page=30}}</ref> |
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<math>a_c = \frac{v}{t}\hat{r} = \frac{r\omega}{t}\hat{r} = v\omega = \frac{v^2}{r}</math> |
:<math>a_c = \frac{v}{t}\hat{r} = \frac{r\omega}{t}\hat{r} = v\omega = \frac{v^2}{r}</math> |
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tako da za centripetalnu silu važi: |
tako da za centripetalnu silu važi: |
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<math>F_c = ma_c = \frac{m v^2}{r}</math> |
:<math>F_c = ma_c = \frac{m v^2}{r}</math> |
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:<math display="block" qid=Q2248131>a_c = \lim_{\Delta t \to 0} \frac{|\Delta \textbf{v}|}{\Delta t}</math> |
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{{rut}} |
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where <math>\Delta \textbf{v}</math> is the [[Euclidean vector#Addition and subtraction|difference]] between the velocity vectors. Since the velocity vectors in the above diagram have constant magnitude and since each one is perpendicular to its respective position vector, simple vector subtraction implies two similar isosceles triangles with congruent angles – one comprising a [[base (geometry)|base]] of <math>\Delta \textbf{v}</math> and a [[isosceles triangle|leg]] length of <math>v</math>, and the other a [[base (geometry)|base]] of <math>\Delta \textbf{r}</math> (position vector [[Euclidean vector#Addition and subtraction|difference]]) and a [[isosceles triangle|leg]] length of <math>r</math>:<ref name="uniform_circular_motion">{{cite web |author=OpenStax CNX|title=Uniform Circular Motion |url=https://courses.lumenlearning.com/suny-osuniversityphysics/chapter/4-4-uniform-circular-motion/ }}</ref> |
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<math display="block">\frac{|\Delta \textbf{v}|}{v} = \frac{|\Delta \textbf{r}|}{r}</math> |
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<math display="block">|\Delta \textbf{v}| = \frac{v}{r}|\Delta \textbf{r}|</math> |
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Therefore, <math>|\Delta\textbf{v}|</math> can be substituted with <math>\frac{v}{r} |\Delta \textbf{r}|</math>:<ref name="uniform_circular_motion" /> |
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<math display="block">a_c = \lim_{\Delta t \to 0} \frac{|\Delta \textbf{v}|}{\Delta t} = \frac{v}{r} \lim_{\Delta t \to 0} \frac{|\Delta \textbf{r}|}{\Delta t} = \omega\lim_{\Delta t \to 0} \frac{|\Delta \textbf{r}|}{\Delta t} = v\omega = \frac{v^2}{r}</math> |
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The direction of the force is toward the center of the circle in which the object is moving, or the [[osculating circle]] (the circle that best fits the local path of the object, if the path is not circular).<ref> |
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{{cite book |
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| title = Experimental physics |
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|author1=Eugene Lommel |author2=George William Myers | publisher = K. Paul, Trench, Trübner & Co |
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| year = 1900 |
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| page = 63 |
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| url = https://books.google.com/books?id=4BMPAAAAYAAJ&pg=PA63 |
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}}</ref> |
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The speed in the formula is squared, so twice the speed needs four times the force. The inverse relationship with the radius of curvature shows that half the radial distance requires twice the force. |
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== Centripetalna sila izražena preko ugaonih veličina == |
== Centripetalna sila izražena preko ugaonih veličina == |
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== Centripetalna sila kod relativističkog kretanja == |
== Centripetalna sila kod relativističkog kretanja == |
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U [[Акцелератор|akceleratorima čestica]], brzina čestica može biti veoma visoka (uporediva sa [[Брзина светлости|brzinom svetlosti u vakuumu]]). Za kretanje kod tako velikih relativističkih brzina ne važi klasična mehanika, već se mora koristiti [[Specijalna teorija relativnosti|fizika specijalne relativnosti]]. |
U [[Акцелератор|akceleratorima čestica]], brzina čestica može biti veoma visoka (uporediva sa [[Брзина светлости|brzinom svetlosti u vakuumu]]). Za kretanje kod tako velikih relativističkih brzina ne važi klasična mehanika, već se mora koristiti [[Specijalna teorija relativnosti|fizika specijalne relativnosti]]. |
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Izraz za centripetalnu silu pri relativističkom kretanju je:<ref>{{cite book |title=An Introduction to the Physics of Particle Accelerators |first1=Mario |last1=Conte |first2=William W |last2=Mackay |publisher=World Scientific |year=1991 |isbn=978-981-4518-00-0 |page=8 |url=https://books.google.com/books?id=yJrsCgAAQBAJ}} [https://books.google.com/books?id=yJrsCgAAQBAJ&pg=PA8 Extract of page 8]</ref> |
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Izraz za centripetalnu silu pri relativističkom kretanju je: |
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:<math>F_c = \frac{\gamma m v^2}{r} = \gamma m v \omega</math> |
:<math>F_c = \frac{\gamma m v^2}{r} = \gamma m v \omega</math> |
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:<math>\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}</math> |
:<math>\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}</math> |
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[[Lorencov faktor]].<ref name=Forshaw>{{cite book |title=Dynamics and Relativity |first1=Jeffrey |last1=Forshaw |first2=Gavin |last2=Smith |publisher=[[John Wiley & Sons]] |year=2014 |isbn=978-1-118-93329-9 |url=https://books.google.com/books?id=5TaiAwAAQBAJ}}</ref><ref>[http://www.nap.edu/html/oneuniverse/motion_knowledge_concept_12.html One universe], by [[Neil deGrasse Tyson]], [[Charles Tsun-Chu Liu]], and Robert Irion.</ref> |
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[[Lorencov faktor]]. |
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== Izvori == |
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[[File:Centripetal force diagram.svg|thumb|A body experiencing [[uniform circular motion]]<ref>{{cite book |title=Elements of Newtonian mechanics: including nonlinear dynamics |edition=3 |first1=Jens M. |last1=Knudsen |first2=Poul G. |last2=Hjorth |publisher=Springer |year=2000 |isbn=3-540-67652-X |page=96 |url=https://books.google.com/books?id=Urumwws_lWUC&pg=PA96 }}</ref> requires a centripetal force, towards the axis as shown, to maintain its circular path.]] |
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In the case of an object that is swinging around on the end of a rope in a horizontal plane, the centripetal force on the object is supplied by the tension of the rope. The rope example is an example involving a 'pull' force. The centripetal force can also be supplied as a 'push' force, such as in the case where the normal reaction of a wall supplies the centripetal force for a [[wall of death (motorcycle act)|wall of death]] or a [[Rotor (ride)|Rotor]] rider. |
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[[Isaac Newton|Newton]]'s idea of a centripetal force corresponds to what is nowadays referred to as a [[central force]]. When a [[satellite]] is in [[orbit]] around a [[planet]], gravity is considered to be a centripetal force even though in the case of eccentric orbits, the gravitational force is directed towards the focus, and not towards the instantaneous center of curvature.<ref> |
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{{cite book |
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| title = In Quest of the Universe |
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| edition = 6th |
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| author = Theo Koupelis |
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| publisher = Jones & Bartlett Learning |
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| year = 2010 |
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| isbn = 978-0-7637-6858-4 |
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| page = 83 |
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| url = https://books.google.com/books?id=GVlpKZ67DscC&pg=PA83 |
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}}</ref> |
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Another example of centripetal force arises in the helix that is traced out when a charged particle moves in a uniform [[magnetic field]] in the absence of other external forces. In this case, the magnetic force is the centripetal force that acts towards the helix axis. |
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== Primeri == |
== Primeri == |
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== Literatura == |
== Literatura == |
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{{Refbegin}} |
{{Refbegin|30em}} |
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* {{cite book |
* {{cite book |
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|author1=Serway, Raymond A. |author2=Jewett, John W. | title = Physics for Scientists and Engineers |
|author1=Serway, Raymond A. |author2=Jewett, John W. | title = Physics for Scientists and Engineers |
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}} |
}} |
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* [https://web.archive.org/web/20180804151453/http://regentsprep.org/Regents/physics/phys06/bcentrif/default.htm Centripetal force] vs. [https://web.archive.org/web/20180804144558/http://regentsprep.org/Regents/physics/phys06/bcentrif/centrif.htm Centrifugal force], from an online Regents Exam physics tutorial by the Oswego City School District |
* [https://web.archive.org/web/20180804151453/http://regentsprep.org/Regents/physics/phys06/bcentrif/default.htm Centripetal force] vs. [https://web.archive.org/web/20180804144558/http://regentsprep.org/Regents/physics/phys06/bcentrif/centrif.htm Centrifugal force], from an online Regents Exam physics tutorial by the Oswego City School District |
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* {{cite book |title=The variational principles of mechanics |last=Lanczos |first=Cornelius |page=Introduction, pp. xxi–xxix |edition=4th |publisher=Dover Publications Inc. |location= New York |isbn=0-486-65067-7 |year=1970 |url=https://books.google.com/books?id=ZWoYYr8wk2IC&pg=PR4 |no-pp=true}} |
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* {{Cite book |last=Synge |first=J. L. |url=http://link.springer.com/10.1007/978-3-642-45943-6 |title=Principles of Classical Mechanics and Field Theory / Prinzipien der Klassischen Mechanik und Feldtheorie |date=1960 |publisher=Springer Berlin Heidelberg |isbn=978-3-540-02547-4 |editor-last=Flügge |editor-first=S. |series=Encyclopedia of Physics / Handbuch der Physik |volume=2 / 3 / 1 |location=Berlin, Heidelberg |chapter=Classical dynamics |doi=10.1007/978-3-642-45943-6 |oclc=165699220}} |
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* {{cite book |title=Mathematical methods of classical mechanics |last=Arnolʹd |first=VI |year=1989 |publisher=Springer |edition=2nd |page= Chapter 8 |isbn=978-0-387-96890-2 |url=https://books.google.com/books?id=Pd8-s6rOt_cC |no-pp=true}} |
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* {{cite book |title=Geometric algebra for physicists |last1=Doran |first1=C |last2=Lasenby |first2=A |publisher=Cambridge University Press |page=§12.3, pp. 432–439 |isbn=978-0-521-71595-9 |year=2003 |url=http://www.worldcat.org/search?q=9780521715959&qt=owc_search}} |
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* {{cite web|last=Merrifield|first=Michael|title=γ – Lorentz Factor (and time dilation)|url=http://www.sixtysymbols.com/videos/lorentz.htm|work=Sixty Symbols|publisher=[[Brady Haran]] for the [[University of Nottingham]]}} |
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* {{cite web|last=Merrifield|first=Michael|title=γ2 – Gamma Reloaded|url=http://www.sixtysymbols.com/videos/gamma_reloaded.htm|work=Sixty Symbols|publisher=[[Brady Haran]] for the [[University of Nottingham]]}} |
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* {{cite journal| last1=Gomez|first1=R W|last2=Hernandez-Gomez|first2=J J|last3=Marquina|first3=V|date=25 July 2012|title=A jumping cylinder on an inclined plane|url=https://www.researchgate.net/publication/236030807|journal=Eur. J. Phys.|publisher=IOP| volume=33|issue=5| pages=1359–1365|doi=10.1088/0143-0807/33/5/1359| access-date=25 April 2016| arxiv = 1204.0600 | bibcode = 2012EJPh...33.1359G | s2cid=55442794}} |
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{{refend}} |
{{refend}} |
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Верзија на датум 18. октобар 2022. у 06:36
Centripetalna sila (od latinskih reči centrum, „centar” i petere, „tražiti”[1]) je sila koja uzrokuje da telo sledi zakrivljenu putanju. Njen pravac je uvek ortogonalan na vektor brzine tela u datoj tački i usmeren je prema centru zakrivljenosti putanje.
Najjednostavniji slučaj delovanja centripetalne sile je kružno kretanje u kojem se telo kreće konstantnom brzinom po kružnici. Centripetalna sila je u ovom slučaju usmerena duž poluprečnika kruga od tačke u kojoj se telo u datom trenutku nalazi ka centru kruga.[2][3]
Matematički opis kretanja tela po kružnoj putanji izveo je holandski fizičar Kristijan Hajgens 1659. godine.[4] Isak Njutn je centripetalnu silu opisao kao „silu kojom se tela povlače ili prisiljavaju, ili na bilo koji način teže ka tački kao centru”.[5] U Njutnovoj mehanici, sila gravitacija je centripetalna sila koja je odgovorna za orbitalna kretanja planeta, satelita, itd.
Pojam centrifugalne sile se objašnjava preko centripetalne sile. Centripetalna sila je realna sila koja deluje na telo pri kružnom kretanju gledano iz stacionarnog inercijalnog sistema referencije. U pokretnom neinercijalnom sistemu referencije vezanom za telo koje rotira, ne vidi se centripetalna sila, ali da bi se objasnilo kretanje tela uvodi se centrifugalna sila koja ima isti intenzitet i pravac kao centripetalna sila, ali je suprotnog smera u odnosu na centripetalnu silu i usmerena je od centra zakrivljene putanje ka telu.
Formula
Centripetalna sila koja deluje na objekt mase m koji se kreće po kružnici je zadata Drugim Njutnovim zakonom:
gde je centripetalno ubrzanje koje se za telo koje se kreće tangencijalnom brzinom v duž puta radijusa zakrivljenosti r može izračunati kao:[6]
tako da za centripetalnu silu važi:
Један корисник управо ради на овом чланку. Молимо остале кориснике да му допусте да заврши са радом. Ако имате коментаре и питања у вези са чланком, користите страницу за разговор.
Хвала на стрпљењу. Када радови буду завршени, овај шаблон ће бити уклоњен. Напомене
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where is the difference between the velocity vectors. Since the velocity vectors in the above diagram have constant magnitude and since each one is perpendicular to its respective position vector, simple vector subtraction implies two similar isosceles triangles with congruent angles – one comprising a base of and a leg length of , and the other a base of (position vector difference) and a leg length of :[7]
Centripetalna sila izražena preko ugaonih veličina
Centripetalna sila se ponekad izražava preko ugaone brzine objekta ω koji rotira oko centra kruga. Ugaona brzina je vezana za tangencijalnu brzinu formulom
tako da je centripetalna sila preko ugaone brzine izražena kao:
Centripetalna sila se za periodična kretanja može izraziti i preko perioda T , odnosno vremena potrebnom da telo napravi pun obrt oko centra kruga. Kako je veza između ugaone brzine i perioda , jednačina za centripetalnu silu postaje:
Centripetalna sila kod relativističkog kretanja
U akceleratorima čestica, brzina čestica može biti veoma visoka (uporediva sa brzinom svetlosti u vakuumu). Za kretanje kod tako velikih relativističkih brzina ne važi klasična mehanika, već se mora koristiti fizika specijalne relativnosti.
Izraz za centripetalnu silu pri relativističkom kretanju je:[10]
gde je
Izvori
In the case of an object that is swinging around on the end of a rope in a horizontal plane, the centripetal force on the object is supplied by the tension of the rope. The rope example is an example involving a 'pull' force. The centripetal force can also be supplied as a 'push' force, such as in the case where the normal reaction of a wall supplies the centripetal force for a wall of death or a Rotor rider.
Newton's idea of a centripetal force corresponds to what is nowadays referred to as a central force. When a satellite is in orbit around a planet, gravity is considered to be a centripetal force even though in the case of eccentric orbits, the gravitational force is directed towards the focus, and not towards the instantaneous center of curvature.[14]
Another example of centripetal force arises in the helix that is traced out when a charged particle moves in a uniform magnetic field in the absence of other external forces. In this case, the magnetic force is the centripetal force that acts towards the helix axis.
Primeri
Za telo koje pomoću užeta rotira u horizontalnoj ravni, u ulozi centripetalne sile koja izaziva kružno kretanje tela je sila zatezanja užeta. U ovom slučaju centripetalna sila je sila povlačenja. Centripetalna sila može biti pružena i kao sila guranja, kao u slučaju kada normalna reakcija zida pruža centripetalnu silu vozaču na zidu smrti.
Kada naelektrisana čestica uđe u uniformno magnetno polje pod pravim uglom u odnosu na pravac polja, magnetna sila će biti centripetalna sila za naelektrisanu česticu i u odsustvu drugih spoljašnjih sila, čestica će se kretati po spirali oko magnetnog polja. Kada naelektrisana čestica izgubi svoju brzinu, kretaće se po kružnici oko ose magnetnog polja.
Vidi još
Reference
- ^ Craig, John (1849). A new universal etymological, technological and pronouncing dictionary of the English language: embracing all terms used in art, science, and literature, Volume 1. Harvard University. стр. 291. Extract of page 291
- ^ Russelkl C Hibbeler (2009). „Equations of Motion: Normal and tangential coordinates”. Engineering Mechanics: Dynamics (12 изд.). Prentice Hall. стр. 131. ISBN 978-0-13-607791-6.
- ^ Paul Allen Tipler; Gene Mosca (2003). Physics for scientists and engineers (5th изд.). Macmillan. стр. 129. ISBN 978-0-7167-8339-8.
- ^ P. Germain; M. Piau; D. Caillerie, ур. (2012). Theoretical and Applied Mechanics. Elsevier. ISBN 9780444600202.
- ^ Newton, Isaac (2010). The principia : mathematical principles of natural philosophy. [S.l.]: Snowball Pub. стр. 10. ISBN 978-1-60796-240-3.
- ^ Chris Carter (2001). Facts and Practice for A-Level: Physics. S.2.: Oxford University Press. стр. 30. ISBN 978-0-19-914768-7.
- ^ а б OpenStax CNX. „Uniform Circular Motion”.
- ^ Eugene Lommel; George William Myers (1900). Experimental physics. K. Paul, Trench, Trübner & Co. стр. 63.
- ^ Colwell, Catharine H. „A Derivation of the Formulas for Centripetal Acceleration”. PhysicsLAB. Архивирано из оригинала 15. 08. 2011. г. Приступљено 31. 7. 2011.
- ^ Conte, Mario; Mackay, William W (1991). An Introduction to the Physics of Particle Accelerators. World Scientific. стр. 8. ISBN 978-981-4518-00-0. Extract of page 8
- ^ Forshaw, Jeffrey; Smith, Gavin (2014). Dynamics and Relativity. John Wiley & Sons. ISBN 978-1-118-93329-9.
- ^ One universe, by Neil deGrasse Tyson, Charles Tsun-Chu Liu, and Robert Irion.
- ^ Knudsen, Jens M.; Hjorth, Poul G. (2000). Elements of Newtonian mechanics: including nonlinear dynamics (3 изд.). Springer. стр. 96. ISBN 3-540-67652-X.
- ^ Theo Koupelis (2010). In Quest of the Universe (6th изд.). Jones & Bartlett Learning. стр. 83. ISBN 978-0-7637-6858-4.
Literatura
- Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th изд.). Brooks/Cole. ISBN 978-0-534-40842-8.
- Tipler, Paul (2004). Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics (5th изд.). W. H. Freeman. ISBN 978-0-7167-0809-4.
- Centripetal force vs. Centrifugal force, from an online Regents Exam physics tutorial by the Oswego City School District
- Lanczos, Cornelius (1970). The variational principles of mechanics (4th изд.). New York: Dover Publications Inc. Introduction, pp. xxi–xxix. ISBN 0-486-65067-7.
- Synge, J. L. (1960). „Classical dynamics”. Ур.: Flügge, S. Principles of Classical Mechanics and Field Theory / Prinzipien der Klassischen Mechanik und Feldtheorie. Encyclopedia of Physics / Handbuch der Physik. 2 / 3 / 1. Berlin, Heidelberg: Springer Berlin Heidelberg. ISBN 978-3-540-02547-4. OCLC 165699220. doi:10.1007/978-3-642-45943-6.
- Arnolʹd, VI (1989). Mathematical methods of classical mechanics (2nd изд.). Springer. Chapter 8. ISBN 978-0-387-96890-2.
- Doran, C; Lasenby, A (2003). Geometric algebra for physicists. Cambridge University Press. стр. §12.3, pp. 432–439. ISBN 978-0-521-71595-9.
- Merrifield, Michael. „γ – Lorentz Factor (and time dilation)”. Sixty Symbols. Brady Haran for the University of Nottingham.
- Merrifield, Michael. „γ2 – Gamma Reloaded”. Sixty Symbols. Brady Haran for the University of Nottingham.
- Gomez, R W; Hernandez-Gomez, J J; Marquina, V (25. 7. 2012). „A jumping cylinder on an inclined plane”. Eur. J. Phys. IOP. 33 (5): 1359—1365. Bibcode:2012EJPh...33.1359G. S2CID 55442794. arXiv:1204.0600 . doi:10.1088/0143-0807/33/5/1359. Приступљено 25. 4. 2016.
Spoljašnje veze
- Notes from University of Winnipeg
- Notes from Physics and Astronomy HyperPhysics at Georgia State University; see also home page
- Notes from Britannica
- Notes from PhysicsNet
- NASA notes by David P. Stern
- Notes from U Texas.
- Analysis of smart yo-yo
- The Inuit yo-yo
- Kinematic Models for Design Digital Library (KMODDL)