Relation between mass distribution and angular velocity

[songoku]

Homework Statement

How should the mass of a rotating body of radius r be distributed 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

Relevant Equations

Not sure

Is E the correct answer because I think angular velocity is independent of mass distribution of the object?

Thanks

 

[ScienceIsMyLady]

Perhaps it means with the same rotational kinetic energy?
$$\frac{1}{2}I\omega^2$$
With the same rotational kinetic energy, if you want to have higher angular velocity, you want a lower moment of inertia, which does depend on the mass distribution

 

[songoku]

Perhaps it means with the same rotational kinetic energy?
$$\frac{1}{2}I\omega^2$$
With the same rotational kinetic energy, if you want to have higher angular velocity, you want a lower moment of inertia, which does depend on the mass distribution

Then the answer will be C?

Thanks

 

[Herman Trivilino]

Guessing that the question refers to kinetic energy is not a good strategy. There is no mention of kinetic energy in the statement of the question.

Can you help us understand your reasoning for choice E? Saying that mass distribution has no impact on angular velocity because angular velocity is independent of mass distribution is not an explanation, it's just another way of saying the same thing. Why do you think E is the answer?

 

[songoku]

Guessing that the question refers to kinetic energy is not a good strategy. There is no mention of kinetic energy in the statement of the question.

Can you help us understand your reasoning for choice E? Saying that mass distribution has no impact on angular velocity because angular velocity is independent of mass distribution is not an explanation, it's just another way of saying the same thing. Why do you think E is the answer?

At first I imagine there is a particle object at a certain distance from axis of rotation so how fast it rotates does not depend on how the mass is distributed, rather than it depends on how strong the external force making it to turn.

Now I realize that it is not good because the object has radius r so I can not think it as particle. The axis of rotation can also be located through the center of the mass of the object. I also ignored the case whether the mass distribution will affect the angular velocity if external force is constant.

I can imagine that different mass distribution will result different value of moment of inertia for same object but I do not know the relation between mass distribution and angular velocity. If the moment of inertia changes, how will this affect angular velocity?

Thanks

 

[jbriggs444]

I dislike the question because it does not give enough information to say what is being held constant as the mass distribution is allowed to change. We are left to guess.

Rather than rotational kinetic energy (which is not conserved in a closed system), I would guess at angular momentum. Angular momentum is conserved in a closed system.

 

[Herman Trivilino]

If the moment of inertia changes, how will this affect angular velocity?

Have you seen the demonstration (or at least a video of it) where a rotating ice skater brings her arms inward? Or the physics classroom variant where a person stands on a rotating platform with weights held in each hand?

 

[songoku]

I think I get the hint.

Thank you very much scienceismylady, mister T, jbriggs444