Numford

MechanicsClass 11, System of Particles and Rotational Motion

Dimensional formula of Radius of gyration

[L]

Symbolk SI unitmetre (m)

The distance at which all the mass could sit and give the same moment of inertia. It is a length.

Derivation

How to get the dimensional formula of radius of gyration

  1. Start from the definition: radius of gyration = sqrt(moment of inertia / mass).
  2. moment of inertia = mass × length2, so moment of inertia is [M] × [L]2 = [M L2].
  3. Put in the dimension of each part: sqrt([M L2] / [M]).
  4. Add the powers of each base quantity: [L].
Same dimensions

Quantities with the dimensions [L]

Equal dimensions do not make them the same quantity. Compare radius of gyration with the others in the full grid.

Practice

Three questions on radius of gyration

1Which of these has the same dimensions as radius of gyration?

2What is the SI unit of radius of gyration?

3Which one has different dimensions from the others?

Questions

Radius of gyration: quick answers

What is the dimensional formula of radius of gyration?

The dimensional formula of radius of gyration is [L]. It comes from radius of gyration = sqrt(moment of inertia / mass).

What is the SI unit of radius of gyration?

The SI unit of radius of gyration is the metre (m).

Which quantities have the same dimensions as radius of gyration?

Radius of gyration shares [L] with length, displacement, mean free path, wavelength, amplitude, focal length, fringe width, de Broglie wavelength. Equal dimensions do not make them the same quantity.

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