Question 515: Centre of Mass and Rotational Motion

Question

The radius of gyration of a circular disc of radius R and mass m rotating about diameter as axis is

Accepted Answer

To determine the radius of gyration of a circular disc of radius $ R $ and mass $ m $ rotating about its diameter, use the formula for the radius of gyration:
$$ k = \sqrt{\frac{I}{m}} $$
where $ I $ is the moment of inertia of the disc about the diameter, and $ m $ is the mass of the disc.
For a circular disc of mass $ m $ and radius $ R $, the moment of inertia $ I $ about its diameter is given by:
$$ I = \frac{1}{4} m R^2 $$
Substituting the expression for $ I $ into the formula for the radius of gyration:
$$ k = \sqrt{\frac{\frac{1}{4} m R^2}{m}} = \sqrt{\frac{1}{4} R^2} = \frac{R}{2} $$
Therefore, the radius of gyration of the circular disc about its diameter is
Option C
: $\frac{R}{2}$

Answer

$\mathrm{R} \sqrt{2}$

Answer

$\mathrm{R} / \sqrt{2}$

Answer

$\mathrm{R} / 2$

Answer

$\mathrm{R}$

Centre of Mass and Rotational Motion

The radius of gyration of a circular disc of radius R and mass m rotating about diameter as axis is

Choose the correct answer: