Table of translational and rotational motion

Rotational Dynamics, Mechanics, Physics / July 20, 2022 July 26, 2022

Physical Quantities in translational and rotational motion

Below are some physical quantities described in both translational as well as rotational motion. Quantities formula in respective motion, as well as the relation between translational and rotational motion, is also given.

S.N	Physical Quantities	Translational Motion	Rotational Motion	Relation
1.	displacement	$s$ (displacement)	$\theta$ (angular displacement)	–
2.	velocity	$v=\frac{ds}{dt}$ (linear velocity)	$\omega = \frac{d\theta}{dt}$ (angular velocity)	$v = \omega r$
3.	acceleration	$a = \frac{dv}{dt}$ (linear acceleration)	$\alpha = \frac{d\omega}{dt}$ (angular acceleration)	$a = \alpha r$
4.	mass	$m$ (mass)	$I$ (moment of inertia)	$I = \sum_{i=1}^{n} m_i r_i^2$
5.	Force	$F=ma$ (force)	$\tau=I\alpha$ (Torque)	$\overrightarrow{\tau} = \overrightarrow{r} \times \overrightarrow{F}$
6.	momentum	$P=mv$ (linear momentum)	$L=I\omega$ (Angular momentum)	$\overrightarrow{L} = \overrightarrow{r} \times \overrightarrow{P}$
7.	Work	$W = \overrightarrow{F}.\overrightarrow{s}$	$W = \tau \theta$	–
8.	Kinetic Energy	$E = \frac{1}{2}mv^2$	$E = \frac{1}{2}I\omega^2$	–
9.	Power	$P = \overrightarrow{F}.\overrightarrow{v}$	$P=\tau \omega$	–
10.	Impulse	$F\Delta t$	$\tau \Delta t$

Equations of Motion

v = u + at

\omega = \omega_0 + \alpha t

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