Question

How should the mass of a rotating body of radius r be distributed so as to maximize its angular velocity?

• A. The mass should be concentrated at the outer edge of the body
• B. The mass should be evenly distributed throughout the body
• C. The mass should be concentrated at the axis of rotation
• D. The mass should be concentrated at a point midway between the axis of rotation and the outer edge of the body
• E. Mass distribution has no impact on angular velocity

Answer 1

The correct option is C The mass should be concentrated at the axis of rotation

The rotating body is an isolated system ,so its angular momentum is conserved (constant) according to the law of conservation of momentum .The angular momentum $L$ of a body is given by ,

$L=I\omega$ ,

where $I=$ moment of inertia of the body ,

$\omega =$ angular velocity of body ,

now $I=\Sigma m{r}^2$ ,

where $r=$ distance of mass from axis of rotation , (moment of inertia also depends upon the distribution of mass about axis of rotation) ,

now as $L$ is constant ,it means product of moment of inertia $I$ and angular velocity $\omega$ will also be constant , so to maximize the $\omega$ we have to reduce the $I$ , for that we will reduce $r$ , it means the mass should be concentrated at the axis of rotation .