Review before final exam. Guide how to identify type of the problem

Transcription

1 Review before final eam. Guide how to identif tpe of the problem

2 Guide how to identif tpe of the problem The question is about? sas average acceleration or if the acceleration is constant a=dv/dt ma be used acceleration force conditions for sstem at rest a =0 a =0 α=0 The problem is for application of Newton s 2 nd Law: Circular motion? a =v 2 /R for the -ais pointing towards the circle center Does/can center-of-mass of an object move? m a F i (0=) m a F i Usuall a is zero for proper choice of coordinates Does/can an object rotate? I α τ i Also often needed: α=a/r Rolling combines both for the same object τ= ± r F sinθ or ± r - F

3 Wave velocit? v= ω/k =f λ v f = v i v f = v i g t = v i t = v i t 1 / 2 g ( t) 2 angular momentum L tot i =L tot f Etended object: L=Iω Point-like object: L= ± r mv sinθ or ± r - mv velocit Collision? (two objects, there is before and after the interaction ) An rotation involved? linear momentum P tot i =P tot f p=mv In addition, use K i =K f Does the tet sa elastic? sas average velocit or if the velocit is constant v=d/dt ma be used K i +U i =K f +U f Rotating object: K= 1 / 2 Iω 2 solve using energ conservation Linear motion: K= 1 / 2 mv 2 Gravitational: U=mgh Elastic (spring) : U= 1 / 2 k 2 Does the tet sa perfectl inelastic or the objects stick to each other? v 1f =v 2f

4 = v i t = v i t 1 / 2 g ( t) 2 v f = v i v f = v i g t Is velocit constant? = v t position Is acceleration constant? = v i t + 1 / 2 a ( t) 2 v f = v i + a t linear angular v a θ ω α solve using energ conservation K i +U i =K f +U f Rotating object: K= 1 / 2 Iω 2 Linear motion: K= 1 / 2 mv 2 Gravitational: U=mgh Elastic (spring) : U= 1 / 2 k 2

5 Modification of the slide on velocit and position problems Is mechanical Use conservation energ of conserved? mechanical (Is work b energ eternal or n-conservative forces zero?) Use energ-work theorem E tot =W et. or n-cons. E tot f E tot i =W et. or n-cons.

6 = v i t = v i t 1 / 2 g ( t) 2 v f = v i v f = v i g t Is velocit constant? = v t position Is acceleration constant? = v i t + 1 / 2 a ( t) 2 v f = v i + a t linear angular θ v ω a α solve using energ conservation K i +U i =K f +U f Etended object: K= 1 / 2 Iω 2 Point-like object: K= 1 / 2 mv 2 Gravitational: U=mgh Elastic (spring) : U= 1 / 2 k 2 Phsics 211 Sound Waves 29 The question is about? Wave velocit? v = ω/k =f λ v f = v i v f = v i g t = v i t = v i t 1 / 2 g ( t) 2 Point-like object: L= ± r mv sinθ mv velocit Collision? (two objects, there is before and after the interaction ) Does the tet sa elastic? In addition, use K i =K f sas average velocit or if the velocit is constant v=d/dt ma be used solve using energ conservation E tot i =E tot f An rotation involved? K i +U i =K f +U f Etended object: K= 1 / 2 Iω 2 Point-like object: K= 1 / 2 mv 2 angular momentum linear momentum Gravitational: U=mgh L tot i =L tot f Etended object: L=Iω P tot i =P tot f p=mv Elastic (spring) : U= 1 / 2 k 2 Does the tet sa perfectl inelastic or the objects stick to each other? v 1f =v 2f Phsics 211 Sound Waves 28

7 Wave velocit? v = ω/k =f λ v f = v i v f = v i g t = v i t = v i t 1 / 2 g ( t) 2 Point-like object: L= ± r mv sinθ mv velocit Collision? (two objects, there is before and after the interaction ) sas average velocit or if the velocit is constant v=d/dt ma be used An rotation involved? K i +U i =K f +U f Etended object: K= 1 / 2 Iω 2 Point-like object: K= 1 / 2 mv 2 angular momentum linear momentum Gravitational: U=mgh L tot i =L tot f Etended object: L=Iω P tot i =P tot f p=mv Elastic (spring) : U= 1 / 2 k 2 Does the tet sa elastic? In addition, use K i =K f solve using energ conservation Does the tet sa perfectl inelastic or the objects stick to each other? v 1f =v 2f Phsics 211 Sound Waves 28 Guide how to identif tpe of the problem The question is about? sas average acceleration or if the acceleration is constant a=dv/dt ma be used Circular motion? a =v 2 /R for the -ais pointing towards the circle center acceleration The problem is for application of Newton s 2 nd Law: Does/can center-of-mass of an object move? force Does/can an object rotate? I α τ i Also often needed: m a F i (0=) m a F i α=a/r Usuall a is zero for proper choice of coordinates Rolling combines both for the same object conditions for sstem at rest a =0 a =0 α=0 τ= ± r F sinθ F Phsics 211 Sound Waves 27

8 Wave velocit? v = ω/k =f λ v f = v i v f = v i g t = v i t = v i t 1 / 2 g ( t) 2 Point-like object: L= ± r mv sinθ mv velocit Collision? (two objects, there is before and after the interaction ) sas average velocit or if the velocit is constant v=d/dt ma be used An rotation involved? K i +U i =K f +U f Etended object: K= 1 / 2 Iω 2 Point-like object: K= 1 / 2 mv 2 angular momentum linear momentum Gravitational: U=mgh L tot i =L tot f Etended object: L=Iω P tot i =P tot f p=mv Elastic (spring) : U= 1 / 2 k 2 Does the tet sa elastic? In addition, use K i =K f solve using energ conservation Does the tet sa perfectl inelastic or the objects stick to each other? v 1f =v 2f Phsics 211 Sound Waves 28

9 Guide how to identif tpe of the problem The question is about? sas average acceleration or if the acceleration is constant a=dv/dt ma be used acceleration force conditions for sstem at rest a =0 a =0 α=0 The problem is for application of Newton s 2 nd Law: Circular motion? a =v 2 /R for the -ais pointing towards the circle center Does/can center-of-mass of an object move? Does/can an object rotate? I α τ i Also often needed: m a F i (0=) m a F i α=a/r Usuall a is zero for proper choice of coordinates Rolling combines both for the same object τ= ± r F sinθ F Phsics 211 Sound Waves 27

10 Wave velocit? v = ω/k =f λ v f = v i v f = v i g t = v i t = v i t 1 / 2 g ( t) 2 Point-like object: L= ± r mv sinθ mv velocit Collision? (two objects, there is before and after the interaction ) sas average velocit or if the velocit is constant v=d/dt ma be used An rotation involved? K i +U i =K f +U f Etended object: K= 1 / 2 Iω 2 Point-like object: K= 1 / 2 mv 2 angular momentum linear momentum Gravitational: U=mgh L tot i =L tot f Etended object: L=Iω P tot i =P tot f p=mv Elastic (spring) : U= 1 / 2 k 2 Does the tet sa elastic? In addition, use K i =K f solve using energ conservation Does the tet sa perfectl inelastic or the objects stick to each other? v 1f =v 2f Phsics 211 Sound Waves 28

11 Guide how to identif tpe of the problem The question is about? sas average acceleration or if the acceleration is constant a=dv/dt ma be used acceleration force conditions for sstem at rest a =0 a =0 α=0 The problem is for application of Newton s 2 nd Law: Circular motion? a =v 2 /R for the -ais pointing towards the circle center Does/can center-of-mass of an object move? Does/can an object rotate? I α τ i Also often needed: m a F i (0=) m a F i α=a/r Usuall a is zero for proper choice of coordinates Rolling combines both for the same object τ= ± r F sinθ F Phsics 211 Sound Waves 27