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Conceptual Physics Rotational Motion Conceptual Physics Rotational Motion Lana Sheridan De Anza College July 17, 2017 Last time • energy sources discussion • collisions (elastic) Overview • inelastic collisions • circular motion and rotation • centripetal force • fictitious forces • torque • moment of inertia • center of mass • angular momentum Inelastic collisions are collisions in which energy is lost as sound, heat, or in deformations of the colliding objects. When the colliding objects stick together afterwards the collision is perfectly inelastic. Types of Collision There are two different types of collisions: Elastic collisions are collisions in which none of the kinetic energy of the colliding objects is lost. (Ki = Kf ) When the colliding objects stick together afterwards the collision is perfectly inelastic. Types of Collision There are two different types of collisions: Elastic collisions are collisions in which none of the kinetic energy of the colliding objects is lost. (Ki = Kf ) Inelastic collisions are collisions in which energy is lost as sound, heat, or in deformations of the colliding objects. Types of Collision There are two different types of collisions: Elastic collisions are collisions in which none of the kinetic energy of the colliding objects is lost. (Ki = Kf ) Inelastic collisions are collisions in which energy is lost as sound, heat, or in deformations of the colliding objects. When the colliding objects stick together afterwards the collision is perfectly inelastic. Inelastic Collisions For general inelastic collisions, some kinetic energy is lost. But we can still use the conservation of momentum: pi = pf 9.4 Collisions in One Dimension 257 In contrast, the total kinetic energy of the system of particles may or may not be con- served, depending on the type of collision. In fact, collisions are categorized as being either elastic or inelastic depending on whether or not kinetic energy is conserved. An elastic collision between two objects is one in which the total kinetic energy (as well as total momentum) of the system is the same before and after the collision. Collisions between certain objects in the macroscopic world, such as billiard balls, are only approximately elastic because some deformation and loss of kinetic 9.4energy Collisions in One Dimension 257 take place. For example, you can hear a billiard ball collision, so you know that some of the energy is being transferred away from the system by sound. An elastic In contrast, the total kinetic energy of the system of particles may or may not be con- collision mustserved, be perfectly depending silent! on the Truly type ofelastic collision. collisions In fact, occurcollisions between are categorized atomic andas being subatomic particles.either elastic These or inelastic collisions depending are described on whether by or the not isolated kinetic energy system is model conserved. for both energy andAn elasticmomentum. collision Furthermore, between two objects there ismust one inbe which no transformation the total kinetic energyof kinetic energy(as wellinto as other total typesmomentum) of energy of the within system the is thesystem. same before and after the collision. An inelasticCollisions collision between is one certain in which objects the intotal the kineticmacroscopic energy world, of the such system as billiard is not balls, the same beforeare only and approximately after the collision elastic because (even thoughsome deformation the momentum and loss of of the kinetic system energy is conserved).take Inelastic place. For collisions example, are you of cantwo hear types. a billiardWhen theball objectscollision, stick so you together know that Pitfall Prevention 9.2 after they collide,some of as the happens energy whenis being a meteoritetransferred collides away from with the the system Earth, by thesound. collision An elastic Inelastic Collisions Generally, inelastic collisions are hard to is called perfectlycollision inelastic. must be perfectly When thesilent! colliding Truly elastic objects collisions do not occur stick between together atomic but and subatomic particles. These collisions are described by the isolated system model for analyze without additional infor- some kineticboth energy energy is transformedand momentum. or transferred Furthermore, away, there as mustin the be caseno transformation of a rubber of mation. Lack of this information ball collidingkinetic with energya hard into surface, other typesthe collision of energy is within called the inelastic system. (with no modify- appears in the mathematical representation as having more ing adverb). WhenAn inelastic the rubber collision ball is collides one in which with thethe totalhard kinetic surface, energy some of of the the system ball’s is not unknowns than equations. kinetic energythe issame transformed before and whenafter thethe collision ball is deformed(even though while the itmomentum is in contact of the with system the surface.is Inelastic conserved). collisions Inelastic are collisions described are ofby twothe types.momentum When the version objects of stick the togetheriso- Pitfall Prevention 9.2 after they collide, as happens when a meteorite collides with the Earth, the collision Inelastic Collisions Generally, lated system model. The system could be isolated for energy, with kinetic energy inelastic collisions are hard to transformedis to called potential perfectly or internal inelastic. energy. When Ifthe the colliding system isobjects nonisolated, do not stick there together could but analyze without additional infor- be energy leavingsome kinetic the system energy byis transformedsome means. or Intransferred this latter away, case, as inthere the casecould of alsoa rubber mation. Lack of this information ball colliding with a hard surface, the collision is called inelastic (with no modify- appears in the mathematical be some transformation of energy within the system. In either of these cases, the representation as having more kinetic energying ofadverb). the system When changes. the rubber ball collides with the hard surface, some of the ball’s kinetic energy is transformed when the ball is deformed while it is in contact with unknowns than equations. In the remainderthe surface. of Inelasticthis section, collisions we investigate are described the by mathematical the momentum details version for of col the- iso- lisions in onelated dimension system model. and Theconsider system the could two be extreme isolated cases,for energy, perfectly with kineticinelastic energy and elastic collisions.transformed to potential or internal energy. If the system is nonisolated, there could be energy leaving the system by some means. In this latter case, there could also Perfectly beInelastic some transformation Collisions of energy within the system. In either of these cases, the kinetic energy of the system changes. S S Consider two particlesIn the remainder of masses of mthis1 and section, m2 moving we investigate with initial the mathematical velocities v 1detailsi and vfor2i col- along the samelisions straight in one line dimension as shown and in consider Figure 9.6.the Thetwo extremetwo particles cases, collideperfectly head- inelastic S on, stick together,and elastic and collisions. then move with some common velocity v f after the collision. Because the momentum of an isolated system is conserved in any collision, we can Before the collision, the say that the Perfectlytotal momentum Inelastic before Collisions the collision equals the total momentum of the particles move separately. composite system after the collision: S S Consider two particles of masses m1 and m2 moving with initial velocities v 1i and v 2i S S S S S S alongDp 5 the 0 same S straightpi 5 pf line S as mshown1 v 1i 1in mFigure2 v 2i 5 9.6.m The1 1 twom2 particlesv f collide(9.14) head- S S S on, stick together, and then move with some common velocity v f after the collision. v1i v2i Solving for the final velocity gives m1 m Because the momentum of an isolated system is conserved1 in2 any collision, we can Before the collision, the2 S 1 S Perfectly Inelastic Collisions say that the total momentumS m before1 v 1i them 2collisionv 2i equals the total momentum of the a particles move separately. composite system afterv thef 5 collision: (9.15) m1 1 m2 S S S S S S Dp 5 0 S pi 5 pf S m1 v 1i 1 m2 v 2i 5 m1 1 m2 v f (9.14) After theS collision,S the v1i v2i Solving for the final velocity gives m1 Elastic Collisions 1 2 particles move together.m2 S S m1 v 1i 1 m2 v 2i S S a Consider two particles of masses m1 and mS2 moving with initial velocities v 1i and v 2i v f 5 (9.15) along the same straight line as shown in Figure m9.71 1 onm 2page 258. The two particles S S collide head-on and then leave the collision site with different velocities, v 1f and After the collision,v fthe S m ϩ m v2f . In an elasticElastic collision, Collisions both the momentum and kinetic energy of the system particles1 move2 together. S S are conserved.Consider Therefore, two particles considering of masses velocities m1 and m along2 moving the with horizontal initial velocities direction v 1i andin v 2i b Figure 9.7, wealong have the same straight line as shown in Figure 9.7 on page 258. The two particlesNow the two particles stick together after colliding ) same final velocity!S S collide head-on and then leave the collision site with different velocities, v 1f and Figure 9.6 Schematic reprevf - S p 5 p S m v 1 m v 5 m v 1 m v (9.16) m ϩ m v2f . Ini an elasticf collision,1 1i both2 2i the momentum1 1f 2 2 fand kinetic energy of the system sentation of a perfectly1 2 inelastic head-onpi = pf collision) m1v 1betweeni + m2v2i two= (m 1 + m2)vf are conserved. Therefore,1 2 considering1 2 velocities1 2along1 the horizontal2 direction in b FigureKi 59.7, K wef haveS 2m1v1i 1 2m2v2i 5 2m1v1f 1 2m2v2f (9.17) particles.
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