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Review before final exam

Review before final exam. Today: Guide how to identify type of the problem Workshop tomorrow: Do practice problems Tuesday lecture: (attendance optional) See more practice problems solved. conditions for system at rest. force. Only if the problem explicitly

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Review before final exam

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  1. Review before final exam Today: Guide how to identify type of the problem Workshop tomorrow: Do practice problems Tuesday lecture: (attendance optional) See more practice problems solved

  2. conditions for system at rest force Only if the problem explicitly says “average acceleration” or if the acceleration is constant a=Dv/Dt may be used The problem is for application of Newton’s 2nd Law: Does/can center-of-mass of any object move? Does/can any object rotate? Circular motion? Rolling combines both for the same object Guide how to identify type of the problem The question is about? acceleration (linear or angular) ax=0 ay=0 a=0 I a=Siti m ax=Si Fi x Also often needed: a=a/R ax=v2/R for the x-axis pointing towards the circle center m ay=Si Fi y (0=) Usually ay is zero for proper choice of coordinates t= ± r F sinq or± r┴F

  3. Only if the problem explicitly says “average velocity” or if the velocity is constant v=Dx/Dt may be used The question is about? Wave velocity? A free fall problem? (the only force is weight) Some free fall problems are easier to solve using energy conservation Collision? (two objects, there is “before” and “after” the “interaction”) y Use conservation of mechanical energy vfx =vix vfy =viy - g Dt Dx = vixDt Dy = viyDt-1/2g (Dt)2 x Any rotation involved? yes no Use conservation of angular momentum Use conservation of linear momentum Does the text say “perfectly” inelastic or the objects stick to each other ? Does the text say “elastic” ? no In addition, use Ki=Kf yes yes v1f=v2f velocity (linear or angular) v= w/k =f l Etot i=Etot f Ki +Ui =Kf +Uf Extended object: K= 1/2Iw2 Point-like object: K= 1/2mv2 Gravitational: U=mgh Elastic (spring) : U= 1/2kx2 Ltot i=Ltot f Ptot i=Ptot f p=mv Extended object: L=Iw Point-like object: L= ± r mv sinq or± r┴mv

  4. A free fall problem? (the only force is weight) Some free fall problems are easier to solve using energy conservation Dx = vixDt Dy = viyDt-1/2g (Dt)2 vfx =vix vfy =viy - g Dt Use conservation of mechanical energy Etot i=Etot f Ki +Ui =Kf +Uf y x Extended object: K= 1/2Iw2 Point-like object: K= 1/2mv2 Is velocity constant? Gravitational: U=mgh Elastic (spring) : U= 1/2kx2 Is acceleration constant? The question is about? position (linear or angular) Dx = v Dt Dx = vi Dt + 1/2a (Dt)2 vf =vi + a Dt linear a angular x v a q a w a

  5. … Use conservation of mechanical energy yes no Use energy-work theorem Use conservation of mechanical energy Modification of the slide on “velocity” and “position” problems Is mechanical energy conserved? (Is work by external or non-conservative forces zero?) Etot i=Etot f DEtot =Wext. or non-cons. Etot f - Etot i =Wext. or non-cons.

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