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Physics LibreTexts

6.9: Summary of Linear and Angular Analogs

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Putting it all together

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. 

Summary Listing Fundamental Concepts Used in Mechanics Emphasizing Translational and Rotational Counterparts
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
J1 on 2=J2 on 1

if τnet=0,then ΔL=0

τnet=Iα or τnet=dLdt

τ1 on 2=τ2 on 1
ang J1 on 2=ang J2 on 1

 
Energy

 Kinetic Energy

Work

 

KE=12mv2

W=x2x1Fds

KE=12Iω2

W=θ2θ1τdθ

 

Contributors


This page titled 6.9: Summary of Linear and Angular Analogs is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Dina Zhabinskaya.

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