6.9: Summary of Linear and Angular Analogs
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The chart on below shows all of the linear motion and dynamic variables along with their rotational counterparts. Keep this chart out and handy for ready reference to help you from getting “lost” in all the symbols. You should make sure that you recognize the meaning behind the symbols when you see on of these relationships.
Category | Concept | Translation | Rotation | Relation |
---|---|---|---|---|
Kinematic Variables |
Position Velocity Acceleration |
x v=dxdt a=dvdt |
θ ω=dθdt α=dωdt |
θ=sr ω=vr α=ar |
Fundamental Dynamic Variables |
Force/Torque Mass/Inertia Momentum Impulse Momentum-Impulse |
F m p=mv J=∫Fdt Jext=Δp |
τ I L=Iω ang J=∫τdt ang Jext=ΔL |
τ=rF⊥ I=∑mr2 L=rp⊥
|
Newton's Laws |
First Law Second Law Third Law |
if Fnet=0,then Δp=0 Fnet=ma or Fnet=dpdt F1 on 2=−F2 on 1 |
if τnet=0,then ΔL=0 τnet=Iα or τnet=dLdt τ1 on 2=−τ2 on 1 |
|
Energy |
Kinetic Energy Work
|
KE=12mv2 W=x2∫x1→F⋅d→s |
KE=12Iω2 W=θ2∫θ1→τ⋅d→θ |