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Analogy Between Linear and Rotational Motion

The following table gives a summary of various quantities that describe linear motion and rotational motion.

Linear Motion

 Rotational Motion

Position x

Angle θ

Linear velocity υ =

Angular velocity ω=  

Linear acceleration

Angular acceleration

a=

α=

Mass m

Moment of inertia I

Force F

Torque τ

F=ma

τ =lα

Translational KE =mυ2

Rotational KE = Iω2

Linear momentum P=mυ

Angular momentum L=Iω

Linear momentum of a system is conserved in the absence of net external force

Angular momentum of a system is conserved in the absence of net external torque

Equations of motion

υ=υ0 + at

S = υ0t + at2

υ2 - υ02 = 2ax

Equations of motion

ω = ω0 + αt

θ = ω0t + αt2

ω2 - ω02 = 2αθ





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