Does the mass of a wheel affect the length of time that it spins on an axis?

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A friend and I somehow got on this odd topic and we disagree on the answer. Here's the scenario we were thinking of. If we had 2 wheels that had the same physical dimensions of diameter and width, and the only difference was a considerable difference in mass, would one wheel spin longer on an axis than the other if you gave both of them the same amount of initial force to make them rotate? The bearings would also be the same. A specific example would be a wheel made of a light wood, like balsa, and another wheel made of steel.

I told her I thought the wheel with more mass would spin longer, but she thinks they would spin at the amount of time. I guessed longer because isn't this basically the principle of how a flywheel works? I thought most flywheels were heavy just for this very reason.

And as a separate but related question, does the weight distribution on the disk also make a difference on the length of spinning? So if most of the mass was towards the center, or the edges, or evenly distributed throughout, does this affect the spin times?

I vaguely remember discussing this in physics class in high school, but that was over 30 years ago.

The important matter is that whoever wins gets a bottle of wine. :)

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If one wheel is made from a denser material than the other it will have a higher moment of inertia. If you apply the same torque to start them rotating you will give them the same amount of angular momentum, but the lighter one will rotate faster because it has a smaller moment of inertia. If you apply the same torque to slow them down then they will both slow down at the same time.

Torque is the change in angular momentum so if you apply the same torque, they have the same change in angular momentum. You should only get a difference if (a) the torques are different (eg. if the bearing friction is dependant on wheel speed or weight) or (b) if the length of time the forces are being applied varies.

The mass distribution should not affect the time either. It will strongly affect the moment of inertia but that will simply mean the same torque causes the wheel to spin faster. You will still get the same angular momentum, so the torque from the bearings should still take exactly the same amount of time to slow it down.

I guess it depends how strict you wanna be regarding the conditions of the experiment...

If you use external force/work (whatever it takes) to spin both wheels to the same speed and then let go....the wheel with the larger mass will spin the longest...then, again, you actually ended up putting more energy into it because it has more mass, since both end up at the same speed but the one with more mass now has more kinetic energy.

If you use a controlled force/work to put a finite amount of energy, and the same, you will probably end up using a force of constant magnitude for a given amount of time to put this energy into each wheel....then I think the wheels will simply get back to zero speed in a 'reverse' manner, if you know what I mean, and come to rest at the same time.

So, I think your friend kind of wins since from your statement you guys stated "same initial force"

And as a separate by related answer....

Does the weight distribution make a difference on the length of spinning?

The short answer is "yes", in that it is best to simply have the mass towards the outer radius...you want to store kinetic energy and the fastest moving particles are found towards the outer radius...mass towards to center of rotation does not move that fast and therefore is not worth having around there....

The "long" answer is "it depends" ...again, as mentioned above, what the comparison entails...did you put the same amount of energy into two wheels ? or do you leave them at the same initial speed?

We didn't take into consideration that the same initial force on both wheels would cause them to have a different initial speeds due to their mass difference. We made an assumption that the same force would initiate the same speed for both wheels. So I suppose I will have to ask her what we really meant. Although for me, it would make more sense that we get both wheels spinning at the same speed initially, regardless of how much energy it takes, and then do the timing of how long they would both spin.