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4. Moviment Circular Uniforme
Un moviment circular, és aquell on l’objecte es mou al
voltant d’un cercle de radi constant R. Alguns exemples....
Acceleradors de partícules.
Rodes
Òrbites
Conducció en trams amb corbes
Fones (i llançament
d’objectes varis)
Anàlisi qualitatiu del moviment circular:
T= 7 dies T= 14 dies
https://phet.colorado.edu/sims/html/gravity-and-orbits/latest/gravity-and-orbits_en.html
T= 21 dies T= 28 dies
Què observem:
• El radi es manté constant.
• La velocitat (vector verd) canvia de direcció tota l’estona i és tangent a la direcció del moviment
(només toca la circumferència en 1 punt).
• La longitud (mòdul) de la velocitat no canvia.
• Gira a un ritme constant ( 28 dies 1 volta, 7 dies = ¼ de volta, 14 dies ½ de volta, etc.) recorre
els angles a velocitat constant.
• A diferència del MRU però , el moviment
circular segueix tenint lloc en 2 dimensions.
Per tant, podem recuperar en tot moment les
coordenades x i y fent servir relacions:
Exemple: Un satèl·lit amb una òrbita de 900km sobre la terra, ha fet 2 voltes i mitja. Quina longitud ha recorregut?
R=R terra + R òrbita = 6370km + 900km =7270km
circular.ppt
Exemples resolts:
1. Una roda d’un patinet de 30 cm de diàmetre fa 33,3 voltes cada minut.
Calcula la velocitat lineal d’un punt de la perifèria de la roda.
Cal passar les dades a unitats del SI:
R=0,15 m
2. Dos punts A i B d’una roda es troben situats a 1,0 m i 1,5 m de l’eix, respectivament. Si la
velocitat lineal en B es 1,0 m/s, calcula la velocitat lineal en A i les velocitats angulars en A i B.
3. Un disc que te 15 cm de radi gira a 20 rpm. Calcula:
a) La seva freqüència i el període.
b) La velocitat lineal de l’extrem del disc.
c) El nombre de voltes que fa en 10 minuts.
d) L’acceleració normal que experimenta un punt a 10 cm del centre.
R=0,15 m
Reescrivim tot a les unitats que toquen:
b) La velocitat lineal de l’extrem del disc:
68. Amb el moviment circular és pot simular la gravetat
de manera artificial ja que és necessària una acceleració
normal. A quina velocitat angular hauria de girar un
aspirant d’astronauta per tal de provar si pot resistir una
acceleració de 5 g’s (5 vegades la gravetat terrestre)? A
quina velocitat lineal és mou el seu cos?
Problemes per fer:
i si hi ha uniforme, hi ha moviment circular accelerat!
Com que l’acceleració total ha quedat dividida en 2 components a 90º, per trobar l’acceleració total,
podem aplicar Pitàgores:
R = 0,4m
Problemes de moviment circular accelerat:
79. Els plats que formen el disc dur d’un ordinador giren a 8750 rpm. Aquests plats de 6,00 cm
de radi assoleixen aquesta velocitat de gir en 3,00 s; en canvi, realitzen l’aturada en 1,00 s.
Calcula:
a) La velocitat d’un punt de la periferia del disc despres de l’arrencada. R: 55,0 m/s
b) Les voltes que fa el disc per reproduir un video de 3,00 min. R: 2,6・104 voltes
c) L’acceleracio total a l’instant en que comenca la frenada. R: 5,04・104 m/s2

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circular.ppt

  • 1. 4. Moviment Circular Uniforme Un moviment circular, és aquell on l’objecte es mou al voltant d’un cercle de radi constant R. Alguns exemples.... Acceleradors de partícules. Rodes Òrbites Conducció en trams amb corbes Fones (i llançament d’objectes varis)
  • 2. Anàlisi qualitatiu del moviment circular: T= 7 dies T= 14 dies https://phet.colorado.edu/sims/html/gravity-and-orbits/latest/gravity-and-orbits_en.html T= 21 dies T= 28 dies Què observem: • El radi es manté constant. • La velocitat (vector verd) canvia de direcció tota l’estona i és tangent a la direcció del moviment (només toca la circumferència en 1 punt). • La longitud (mòdul) de la velocitat no canvia. • Gira a un ritme constant ( 28 dies 1 volta, 7 dies = ¼ de volta, 14 dies ½ de volta, etc.) recorre els angles a velocitat constant.
  • 3. • A diferència del MRU però , el moviment circular segueix tenint lloc en 2 dimensions. Per tant, podem recuperar en tot moment les coordenades x i y fent servir relacions: Exemple: Un satèl·lit amb una òrbita de 900km sobre la terra, ha fet 2 voltes i mitja. Quina longitud ha recorregut? R=R terra + R òrbita = 6370km + 900km =7270km
  • 5. Exemples resolts: 1. Una roda d’un patinet de 30 cm de diàmetre fa 33,3 voltes cada minut. Calcula la velocitat lineal d’un punt de la perifèria de la roda. Cal passar les dades a unitats del SI: R=0,15 m 2. Dos punts A i B d’una roda es troben situats a 1,0 m i 1,5 m de l’eix, respectivament. Si la velocitat lineal en B es 1,0 m/s, calcula la velocitat lineal en A i les velocitats angulars en A i B.
  • 6. 3. Un disc que te 15 cm de radi gira a 20 rpm. Calcula: a) La seva freqüència i el període. b) La velocitat lineal de l’extrem del disc. c) El nombre de voltes que fa en 10 minuts. d) L’acceleració normal que experimenta un punt a 10 cm del centre. R=0,15 m Reescrivim tot a les unitats que toquen: b) La velocitat lineal de l’extrem del disc:
  • 7. 68. Amb el moviment circular és pot simular la gravetat de manera artificial ja que és necessària una acceleració normal. A quina velocitat angular hauria de girar un aspirant d’astronauta per tal de provar si pot resistir una acceleració de 5 g’s (5 vegades la gravetat terrestre)? A quina velocitat lineal és mou el seu cos? Problemes per fer:
  • 8. i si hi ha uniforme, hi ha moviment circular accelerat! Com que l’acceleració total ha quedat dividida en 2 components a 90º, per trobar l’acceleració total, podem aplicar Pitàgores:
  • 10. Problemes de moviment circular accelerat: 79. Els plats que formen el disc dur d’un ordinador giren a 8750 rpm. Aquests plats de 6,00 cm de radi assoleixen aquesta velocitat de gir en 3,00 s; en canvi, realitzen l’aturada en 1,00 s. Calcula: a) La velocitat d’un punt de la periferia del disc despres de l’arrencada. R: 55,0 m/s b) Les voltes que fa el disc per reproduir un video de 3,00 min. R: 2,6・104 voltes c) L’acceleracio total a l’instant en que comenca la frenada. R: 5,04・104 m/s2