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

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

The question is about? velocity Only if the problem explicitly says “average velocity” or if the velocity is constant v=  x/  t may be used A free fall problem? (the only force is weight) v fx = v ix v fy = v iy  g  t  x = v ix  t  y = v iy  t      g (  t) 2 x y Collision? (two objects, there is “before” and “after” the “interaction”) Use conservation of mechanical energy L tot i =L tot f Extended object: L=I  Point-like object: L= ± r mv sin  or ± r ┴ mv Any rotation involved? Use conservation of angular momentum yes Use conservation of linear momentum no P tot i =P tot f p=mv Does the text say “elastic” ? In addition, use K i =K f yes v 1f =v 2f yes E tot i =E tot f K i +U i =K f +U f Extended object: K=    I   Point-like object: K=    mv  Gravitational: U=mgh Elastic (spring) : U=    kx 2 (linear or angular) Wave velocity? v =  /k =f Some free fall problems are easier to solve using energy conservation Does the text say “perfectly” inelastic or the objects stick to each other ? no

The question is about?position A free fall problem? (the only force is weight)  x = v ix  t  y = v iy  t      g (  t) 2 v fx = v ix v fy = v iy  g  t x y Is velocity constant? Use conservation of mechanical energy E tot i =E tot f K i +U i =K f +U f Extended object: K=    I   Point-like object: K=    mv  Gravitational: U=mgh Elastic (spring) : U=    kx 2 (linear or angular)  x = v  t  x = v i  t      a (  t) 2 v f = v i  a  t Is acceleration constant? linear  angular xvaxva     Some free fall problems are easier to solve using energy conservation

E tot i =E tot f Modification of the slide on “velocity” and “position” problems Use conservation of mechanical energy yes no Use energy-work theorem  E tot =W ext. or non-cons. E tot f  E tot i =W ext. or non-cons. Use conservation of mechanical energy … Is mechanical energy conserved? (Is work by external or non-conservative forces zero?)