Question 579: Centre of Mass and Rotational Motion

Question

A body of mass 'm' and radius of gyration 'K' has an angular momentum 'L'. Then its angular velocity is

Accepted Answer

To determine the angular velocity of a body with a given mass 'm', radius of gyration 'K', and angular momentum 'L', we need to use the relationship between these quantities. The moment of inertia 'I' of the body is given by:
$$ I = m K^2 $$
Angular momentum 'L' is also related to the moment of inertia 'I' and angular velocity 'ÃÂ' by the following equation:
$$ L = I \omega $$
Substituting the expression for 'I' into the equation for 'L' gives:
$$ L = (m K^2) \omega $$
To solve for the angular velocity 'ÃÂ', we can rearrange this equation:
$$ \omega = \frac{L}{m K^2} $$
Therefore, the correct option for the angular velocity is:
Option A
$$ \frac{\mathrm{L}}{\mathrm{mK}^2} $$

Answer

$$\frac{\mathrm{L}}{\mathrm{mK}^2}$$

Answer

$$\frac{\mathrm{mK}^2}{\mathrm{~L}}$$

Answer

$$\frac{\mathrm{K}^2}{\mathrm{~mL}}$$

Answer

$$\mathrm{mK}^2 \mathrm{~L}$$

Centre of Mass and Rotational Motion

A body of mass 'm' and radius of gyration 'K' has an angular momentum 'L'. Then its angular velocity is

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