3.4 Analogy between translational motion & rotational motion

Physics > Basics of Rotational Motion > 3.0 Kinematics of a plane motion

  Basics of Rotational Motion
    1.0 Rigid body
    2.0 Motion of rigid body
    3.0 Kinematics of a plane motion
    4.0 Moment of inertia
    5.0 Radius of gyration $(K)$
    6.0 Theorems of moment of inertia
    7.0 Moment of inertia of uniform continious rigid bodies
3.4 Analogy between translational motion & rotational motion
S. No.Translational motion

Rotational motion

1.Displacement $\left( {\overrightarrow s } \right)$Angular displacement $\left( {\overrightarrow \theta } \right)$
2.Velocity: $\overrightarrow v = \frac{{d\overrightarrow s }}{{dt}}$Angular velcoity: $\overrightarrow \omega = \frac{{d\overrightarrow \theta }}{{dt}}$
3.Acceleration: $\overrightarrow a = \frac{{d\overrightarrow v }}{{dt}}$Angular acceleration: $\overrightarrow \alpha = \frac{{d\overrightarrow \omega }}{{dt}}$
4.Mass: $M$Moment of inertia: $I$
5.Force: $\overrightarrow F = M\overrightarrow a $Torque: $\overrightarrow \tau = I\overrightarrow \alpha $
6.Work: $dW = \overrightarrow F .\;d\overrightarrow s $Work: $dW = \overrightarrow \tau .\;d\overrightarrow \theta $
7.Kinetic energy of a translational motion, $${K_T} = \frac{1}{2}M{v^2}$$Kinetic energy of a rotational motion, $${K_R} = \frac{1}{2}I{\omega ^2}$$
8.Power: $P = \overrightarrow F .\;\overrightarrow v $Power: $P = \overrightarrow \tau .\;\overrightarrow \omega $
9.Linear momentum: $\overrightarrow p = M\overrightarrow v $Angular momentum: $\overrightarrow L = I\overrightarrow \omega $
10.Equation of translational motion:
  • $\overrightarrow v = \overrightarrow u + \overrightarrow a t$
  • $\overrightarrow s = \overrightarrow u t + \frac{1}{2}\overrightarrow a {t^2}$
  • ${v^2} - {u^2} = 2\overrightarrow a .\;\overrightarrow s $
  • $${\overrightarrow s _{{n^{th}}}} = \overrightarrow u + \frac{{\overrightarrow a }}{2}(2n - 1)$$
Equation of rotational motion
  • $\overrightarrow \omega = \overrightarrow {{\omega _0}} + \overrightarrow \alpha t$
  • $\overrightarrow \theta = \overrightarrow {{\omega _0}} t + \frac{1}{2}\overrightarrow \alpha {t^2}$
  • ${\omega ^2} = \omega _0^2 + 2\overrightarrow \alpha .\;\overrightarrow \theta $
  • ${\overrightarrow \theta _{{n^{th}}}} = {\overrightarrow \omega _0} + \frac{{\overrightarrow a }}{2}(2n - 1)$
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