Answered

A figure skater is spinning slowly with arms outstretched. Shebrings her arms in close to her body and her moment of inertiadecreases by 1/2. Her angular speed increases by a factor of
A. 2
B. 1
C. 4
D. square root of 2
E. 1/2
In the same situation if she decreases her moment of inertiaby a factor of 2, how does her angular speed change?
A. Its reduced by a factor of 4
B. Its reducded by a factor of 2
C. It increases by a factor of 4
D. It increases by a factor of 2
E. It doesnt change
Is the relationship between angular speed and moment ofinertia inversely proportional, or does angular speed have todouble to compensate for any decrease in moment of inertia? I needhelp understanding the relationship between the two. I=2k/omegasquared, correct?



Answer :

The angular speed increases by a factor of 2 and when she decreases her moment of inertia by a factor of 2 her angular speed change.

Angular momentum is a characteristic of rotating bodies determined by the product of their angular velocity and moment of inertia.

  • Angular momentum = Angular velocity x Moment of inertia

The angular momentum is calculated by

L = IW

Where,

I = Inertia momentum

W = angular velocity

It can be calculated by applying the law of conservation of angular momentum as given below:

= [tex]I_{i} W_{i} =I_{f} W_{f}[/tex]

Where, i = initial, f = final

Since the final inertia momentum of figure skater gets decreased by 1/2 from the initial,

= [tex]\frac{1}{2}I_{i} = I_{f}[/tex]

Therefore, the final angular speed would become

 [tex]I_{i} W_{i} = \frac{1}{2} I_{i} W_{f}[/tex]

 [tex]2W_{i} = W_{f}[/tex]

Hence, which means that angular speed increases by a factor 2.

To know more about rotational mechanics visit:

https://brainly.com/question/23160043

#SPJ4

Other Questions