Question

Emmy the trapeze artist flies through the air with her arms and legs stretched out, tumbling head over heels. As she rotates, she pulls her arms and legs close to her chest, as shown in the illustration. 

As Emmy pulls her arms and legs in, how does her rotational inertia change?

it increases

it decreases

it remains constant 

As Emmy pulls her arms and legs in, how does her angular momentum change? 

it increases 

it decreases 

it remains constant 

As Emmy pulls her arms and legs in, how does her rotational speed change? 

it increases 

it decreases 

it remains constant

Answer 1

(a)

In general, the moment of inertia is given by,

$$ I=\text { const } \times M R^{2} $$

When she pulls her arms and legs, the value of \(R\) decreases but mass remain constant. Hence, rotational inertia of Emmy decreases.

(b)

The angular momentum of an isolated system always remains constant.

$$ L=I \omega $$

Hence, angular momentum of Emmy remains constant.

(c)

As the angular momentum is constant,

$$ I_{1} \omega_{1}=I_{2} \omega_{2} $$

Since, the value of \(I_{2}\) decreases, therefore, the value of \(\omega_{2}\) increases to make the angular momentum conserved.

Hence, the angular speed of Emmy increases.