Is there a difference between getting a rotating mass to move compared to a linearly moving mass?

Suppose I have an 8kg bicycle with wheels weighing 2kg and I have an 8kg bicycle, but the wheels weigh only 1.5kg (we assume that the mass is gained at the height of the rims). Will I notice a difference between those 2 bikes when accelerating?

Asker: Rick, 34 years old

Answer

Getting a rotating mass in motion is very similar to getting a linearly moving mass in motion.

The rotating equivalent of mass is called the moment of inertia. More details about this can be found at
http://nl.wikipedia.org/wiki/Traagheidsmoment
In a nutshell it comes down to this: the moment of inertia is proportional to the mass, but also to the square of the distance between this mass and the axis of rotation.
In the case of your example, both bikes weigh 8 kg (in total). We have no difference there.
However, the weight of the rims is different.
mA = 2 kg
mB = 1.5 kg
The distance of the masses to the axis of rotation are the same, because you mention that the mass is considered entirely in the rims. Let’s call this distance R.
The moment of inertia is now the mass multiplied by the square of the distance, so
IA=mA XRXR
IB = mB XRXR
The moment of inertia IA is greater (the case with 2 kg rims) and this bike will start more slowly with the same pedal.
This question is very similar to the next problem. Again, both cases have the same total mass, but there is a difference in moment of inertia:
(copied from http://www.nwo.nl/nwohome.nsf/pages/NWOP_5VGK2S)

You have two eggs of the same size. One egg is hard-boiled, the other is uncooked. You let them roll down a slope at the same time. Which egg goes down first and why?

The uncooked egg.
The boiled egg.
They arrive at the same time.

A is the correct answer

In a boiled egg, all the parts of the egg are solid and connected to each other. This means that all the particles have to start spinning when the egg starts to roll. Energy is needed for that rotation. With an uncooked egg, only the viscous protein directly under the shell will rotate. The rest of the liquid does not rotate, but slides downwards, as it were. With uncooked eggs, less energy will therefore be converted into rotational energy, leaving more energy for the forward movement. This will cause the uncooked egg to roll down faster.

Is there a difference between getting a rotating mass to move compared to a linearly moving mass?

Answered by

dr. ir. Nico Smets

Engineering Sciences

Free University of Brussels
Avenue de la Plein 2 1050 Ixelles
http://www.vub.ac.be/

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