Is my reasoning correct? (rotational kinetic energy)

[lc99]

Homework Statement

Homework Equations

L = IW
RKE = .5IW^2

The Attempt at a Solution

Since the two solid spheres have equal radii and same angular momenta, except that the mass differs, i think that the inertia is equal. However, since sphere A is more heavy, it would spin slower than sphere B, so Sphere B has larger rotational kinetic energy. (ANS: option e)

 

[ehild]

Homework Statement

View attachment 219708

Homework Equations

L = IW
RKE = .5IW^2

The Attempt at a Solution

Since the two solid spheres have equal radii and same angular momenta, except that the mass differs, i think that the inertia is equal. However, since sphere A is more heavy, it would spin slower than sphere B, so Sphere B has larger rotational kinetic energy. (ANS: option e)

The answer is correct, but the reasoning is not.
What do you mean on "Moment"? What is I? does it depend on the mass?

 

[SammyS]

Homework Statement

View attachment 219708

Homework Equations

L = IW
RKE = .5IW^2

The Attempt at a Solution

Since the two solid spheres have equal radii and same angular momenta, except that the mass differs, i think that the inertia is equal. However, since sphere A is more heavy, it would spin slower than sphere B, so Sphere B has larger rotational kinetic energy. (ANS: option e)

While your conclusion may be correct, your reasoning is not correct.

 

[lc99]

While your conclusion may be correct, your reasoning is not correct.

The answer is correct, but the reasoning is not.
What do you mean on "Moment"? What is I? does it depend on the mass?

I'm not too sure either.. that's why i kinda made this post. I'm sort of confused cause i thought that sphere A would have higher rotational inertia since it weighs more. Inertia depends on mass , and the formula for the sphere is 2/5MR^2. Since sphere A has more mass, rotational inertia given by .5mr^2W^2 is higher. But we know that momenta, L = IW , is equal for both spheres. Since they both need to have equal L but sphere A has larger Inertia than sphere B.. this means that B has to make up the momenta by having greater angular velocity.

Sphere A ends up have small angular velocity and so small RKE since RKE depends on angular velocity.

(On another note, I think this sounds more correct. I just had to think in a logical order as i typed this up)

 

[ehild]

I'm not too sure either.. that's why i kinda made this post. I'm sort of confused cause i thought that sphere A would have higher rotational inertia since it weighs more. Inertia depends on mass , and the formula for the sphere is 2/5MR^2. Since sphere A has more mass, rotational inertia given by .5mr^2W^2 is higher. But we know that momenta, L = IW , is equal for both spheres. Since they both need to have equal L but sphere A has larger Inertia than sphere B.. this means that B has to make up the momenta by having greater angular velocity.

Sphere A ends up have small angular velocity and so small RKE since RKE depends on angular velocity.

(On another note, I think this sounds more correct. I just had to think in a logical order as i typed this up)

It is better now. Yes, as A has greater mass than B, and both have the same radius, I, the rotational inertia is greater for A.
The rotational kinetic energy is E_rot =0.5 Iω², but it can be written also as E_rot =0.5 L²/I (as ω=L/I), it is clear which sphere has greater energy.