Why Can't I Get the Correct Answer Using Energy to Calculate Rotational Inertia?

[Pochen Liu]

Homework Statement

How come I can't get the correct answer using Energy as a way to solve this?

Homework Equations

3. The Attempt at a Solution [/B]
The answers use conservation of momentum which makes perfect sense and I understand that, however I used an energy approach where E(flywheel) = E(HST)

So E(flywheel) = 0.5 * 43.2 * 3.22^2 = 223.967J
E(HST) = 0.5 * I * 0.07539^2 (I know this is the correct angular velocity from the answers)

When I solve this I = 78807.427 Kgm^2, the answer is 1850.

What am I doing wrong conceptually? And what have I done, as in, if given a different situation where would have my working have resulted in the correct answer?

 

[Orodruin]

What makes you think energy should be the same for the flywheel and for HST?

 

[Pochen Liu]

Because when I throw a ball into the air the Ek is converted into Eg and then all (most of it) is converted back into Ek as it falls back down, so shouldn't this apply to E(rotational) too?

 

[Orodruin]

Because when I throw a ball into the air the Ek is converted into Eg and then all (most of it) is converted back into Ek as it falls back down, so shouldn't this apply to E(rotational) too?

But this is not at all what is going on. Initially both HST and the flywheel have an energy of 0. Then internal energy (likely stored in a battery) is used to produce motion. Since rotational energy cannot be negative, the rotational energy after turning on the flywheel is positive for both HST and the flywheel. The conversion of energy is from internal energy in the battery to rotational energy so you cannot assume that rotational energy among the two components is conserved. Furthermore, in your approach the total energy is not conserved since it is 0 at the beginning and non-zero in the rotation. You are just making an ad hoc assumption that the rotational energies of each component must be the same.

What you have is more similar to an excited atom emitting a photon. The excess energy is not split evenly between the photon and the atom. Due to the atom being much heavier, the photon will take (most of) the energy.