what quantities does angular momentum depend upon?
WHAT QUANTITIES DOES ANGULAR MOMENTUM DEPEND UPON?
where Mb is the mass, speak of a ball, and V is the size of thevelocity (the speed).Now the gravitational potential power is the energy that a body has whichcan ultimately be offered to accelerate the body to a bigger magnitude the velocity. Because that example, if I hold a round at armslength in ~ rest, and also let the sphere drop to the Earth, the round willspeed up before hitting the Earth. This potential energy, together I washolding the sphere at rest, isgiven through Egrav=Mbg H, where H is the elevation of the ball over the Earth"s surface,and g, the acceleration top top the earth is g=(GMe/R2e) = 9.8 meters/s2(see the inset number in the discussion of load on our previously packet of notes The Universal legislation of Gravitation ).Now here"s the deal: the gravitational potential energy of the ballat remainder in my extended arm, is same to the best kinetic energythat the ball have the right to have just before it get the ground.As the ball falls, H decreases. Therefore the gravitational power decreases.Where does that go? Well, the rate of the round increases.Thus the kinetic power of the ball boosts from the equationfor kinetic power above. Gravitational potential power is beingconverted into kinetic energy.This is how power is conserved.It is also why you sluggish down and speed up together youtravel up and down in a roller coaster.Is it regular with planets in elliptical orbits aroundthe sun increasing near the the perihelion and also slowing down close to theaphelion? and also Kepler"s second law? A bit much more on the Ball ago to the ball: note that when I drop the ball, that bounces earlier up the slows under as that gravitational potentialenergy is regained. Why go does the ball constantly return come a heightslightly reduced than that from which is was initially dropped?The factor is that there are various other sources of power loss: heat, compression,stresses ~ above the ball itself which can not be regained as gravitational energy.However, as soon as all these energies are included up, their full is equal to thesame together the initial gravitational potential energy.Energy conservation is fundamental. Physics can explain to us only how power in the Universetransforms indigenous one form to another.
Angular momentum Conservation
Objects executing motion roughly a point possess a quantity dubbed ANGULAR MOMENTUM. This is an essential physical quantity because all experimental evidence indicates the angular momentum is rigorously conserved in ourUniverse. It have the right to be transferred, however it cannot be developed or destroyed. Forthe an easy case that a tiny mass executing uniformcircular motion roughly a much largermass (so the we deserve to neglect the effect of the center of mass) the quantity ofangular inert takes a an easy form. Together the adjacent figure illustrates themagnitude that the angular momentum in this case is l = mvrwhere together is the angular momentum, m is the fixed of the little object, v is the size of itsvelocity, and also r is the separation in between the little and big objects.
Ice Skaters and Angular Momentum
This formula indicates oneimportant physical repercussion of angular momentum: because the over formulacan be rearranged to offer v = L/(mr) and L is a constant for an isolatedsystem, the velocity v and also the separation r room inversely correlated. Thus, preservation of angular momentumdemands the a decrease in the separationr it is in accompanied by rise in the velocity v, and vice versa. This important principle carries end to an ext complicatedsystems: generally, because that rotating bodies, if your radii decrease lock mustspin quicker in stimulate to conserve angular momentum. This concept is acquainted intuitively come the ice skater who spins faster when the eight are attracted in, andslower when the arms are extended; although most ice skaters don"t think aboutit explicitly, this an approach of spin control is nothing however an invocation that thelaw of angular inert conservation.Notice how this applies to elliptical planetary orbits.
Because that a world of massive m in one elliptical orbit, preservation of angular momentum means that as the object move closer come the sunlight it speeds up.That is, if r decreases climate v must rise to maintain the same L.Thus close to perihelion it accelerates and near aphelion it slows down.Both power conservation and also angular momentum conservation room importantto planetary orbits.
Hey, wait a minute, why perform the planets have any kind of orbital angular momentum?
Note the the reason planets orbit the sun and do not fall into the sun,is because they have angular momentum and have had this angularmomentum from the time they were formed.The planets can have acquired this angular momentum prior to orafter your formation, but it is believed that they were likelyformed indigenous gas product that was currently orbiting the Sun. Moreon this later.