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 Î¸ |
Linear velocity Ï… = |
Angular velocity Ï‰= |
Linear acceleration |
Angular acceleration |
a= |
Î±= |
Mass m |
Moment of inertia I |
Force F |
Torque Ï„ |
F=ma |
Ï„ =lÎ± |
Translational KE =mÏ…^{2 } |
Rotational KE = IÏ‰^{2} |
Linear momentum P=mÏ… |
Angular momentum L=IÏ‰ |
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 Ï…=Ï…_{0} + at S = Ï…_{0}t + at^{2 } Ï…^{2} - Ï…_{0}^{2} = 2ax |
Equations of motion Ï‰ = Ï‰_{0} + Î±t Î¸ = Ï‰_{0}t + Î±t^{2 } Ï‰^{2} - Ï‰_{0}^{2} = 2Î±Î¸ |