Table of translational and rotational motion

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.NPhysical QuantitiesTranslational MotionRotational MotionRelation
1.displacements (displacement)\theta (angular displacement)
2. velocityv=\frac{ds}{dt} (linear velocity)\omega = \frac{d\theta}{dt} (angular velocity)v = \omega r
3. accelerationa = \frac{dv}{dt} (linear acceleration)\alpha = \frac{d\omega}{dt} (angular acceleration)a = \alpha r
4. massm (mass)I (moment of inertia)I = \sum_{i=1}^{n} m_i r_i^2
5. ForceF=ma (force) \tau=I\alpha (Torque)\overrightarrow{\tau} = \overrightarrow{r} \times \overrightarrow{F}
6.momentumP=mv (linear momentum)L=I\omega (Angular momentum)\overrightarrow{L} = \overrightarrow{r} \times \overrightarrow{P}
7.WorkW = \overrightarrow{F}.\overrightarrow{s}W = \tau \theta
8. Kinetic EnergyE = \frac{1}{2}mv^2E = \frac{1}{2}I\omega^2
9.PowerP = \overrightarrow{F}.\overrightarrow{v}P=\tau \omega
10.ImpulseF\Delta t\tau \Delta t

Equations of Motion

S.NEquation in translational motionEquation in rotational motion
1. v = u + at\omega = \omega_0 + \alpha t
2.v^2 = u^2 + 2as\omega^2 = \omega_0^2 + 2\alpha \theta
3.s = ut + \frac{1}{2}at^2\theta = \omega_0 t + \frac{1}{2}\alpha t^2

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