Is it possible to create linear acceleration using nothing but different moments of inertia beteen a wheel and axle?

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In summary, the concept of creating linear acceleration using different moments of inertia between a wheel and axle involves leveraging the differential rotation speeds of the two components. By varying the moment of inertia, one can achieve a torque imbalance that leads to linear motion. However, practical implementation may face challenges due to friction, energy loss, and the need for external forces to initiate and sustain acceleration. Thus, while theoretically possible, the feasibility of this approach in real-world applications remains questionable.
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BishopBrain
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Is it possible to create linear acceleration using nothing but different moments of inertia beteen a wheel and axle?
The Twisted Metal video game series includes a character aptly named Axel, whose vehicle is just himself strapped to a pair of tractor wheels. This is the guy:

axel.jpg

Most of my friends assume that in real life, he probably wouldn't be able to drive anywhere unless his feet were incredibly heavy, so that gravity would apply torque as his lower half swung forward--similar mechanics to a monocycle.

But one of us claimed that even if Axel's center of mass lay perfectly on the axis of rotation of the big wheels , he would still be able to move a little bit if he were so heavy that the moment of inertia of himself was significantly greater than the moment of inertia for his wheels. Axel would still be spinning sickeningly, but his contraption could move about at least a little bit.

Is this correct? Can two very-different wheels applying torque to one another via an axle generate linear motion from friction, even in the absence of any external forces tangential to the axle? We were skeptical, but couldn't figure out how to set up the system to test the math.
 
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If he's rigidly attached to the wheels and he can flex his body to keep his center of mass forwards of the rotation axis then sure he can roll. He'd flip end for end as he does it, though, and I'm guessing the vehicle acts more like a Segway.

Obviously Segways are possible, but you need a motor.
 
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Welcome!
What are those things attached to the shoulders?
 
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Lnewqban said:
What are those things attached to the shoulders?
Machine guns or missiles, I forget which.

Ibix said:
If he's rigidly attached to the wheels and he can flex his body to keep his center of mass forwards of the rotation axis then sure he can roll. He'd flip end for end as he does it, though, and I'm guessing the vehicle acts more like a Segway.

Obviously Segways are possible, but you need a motor.
Yes, in game he's motorized like a Segway. In-game he's also perfectly upright at all times, which is not terribly realistic...

The crux of my question is, if motorized and if his CoM is always on-axis, is movement possible for Axel. If he has a CoM off-axis, then he clearly can (in any number of ways), and I know how to draw up the free-body diagram to analyze it.
 
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BishopBrain said:
The crux of my question is, if motorized and if his CoM is always on-axis, is movement possible for Axel.
Sure, but the wheel hubs (with him) will spin opposite to the wheels.
 
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There is some similarity with a tight rope walker carrying a pole.

The walker can accelerate his center of gravity rightward or leftward by exerting torque against the pole while his feet exert a counter torque on the rope.
 

FAQ: Is it possible to create linear acceleration using nothing but different moments of inertia beteen a wheel and axle?

Is it possible to create linear acceleration using nothing but different moments of inertia between a wheel and axle?

No, it is not possible to create linear acceleration using only different moments of inertia between a wheel and axle. The conservation of angular momentum and the absence of external forces or torques prevent this from occurring.

What role do moments of inertia play in the motion of a wheel and axle system?

The moments of inertia determine how the mass is distributed relative to the axis of rotation. They affect the rotational acceleration of the wheel and axle system when subjected to a torque, but they do not directly contribute to linear acceleration without an external force.

Can internal forces within a wheel and axle system create linear acceleration?

No, internal forces within a closed system like a wheel and axle cannot create linear acceleration. According to Newton's third law, internal forces cancel each other out, resulting in no net linear force or acceleration.

Is there any way to convert rotational motion to linear motion in a wheel and axle system?

Yes, rotational motion can be converted to linear motion using mechanisms such as gears, pulleys, or rack and pinion systems. However, these mechanisms require external forces or constraints to achieve the conversion.

What principles prevent the creation of linear acceleration using only moments of inertia?

The principles of conservation of linear momentum and conservation of angular momentum prevent the creation of linear acceleration using only moments of inertia. Without an external force or torque, the system cannot generate a net linear force to produce linear acceleration.

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