Understanding the Physics of a Wheel and Axel: Exploring Forces and Movement"

[BrainSalad]

I know that the physics community generally hates this kind of question, though I don't know why. Like Richard Feynman said, you can tell an expert by his reluctance to answer honest but naive questions. Okay, I understand that a wheel and axel can be viewed as a lever system with the fulcrum at the axel. Also as a lever arm with the fulcrum at the point the wheels touch the ground. So, if a force is applied at the axel, parallel to the ground, the lever is turned and the system moves forward, a new point on the wheel continually making contact with the ground. Also, if a torque is applied to an axel which is fixed to the wheels (doesn't turn independently) the system moves forward. This is how a car is propelled, even though the torque comes from within the system. In terms of forces, how does this twisting motion cause this movement? I know the ground reaction force must be the cause, but bear with me. Imagine you have a solid rod with a wheel on each end, to which you are attached so that any force you apply is an internal force (in a seat or something, to simulate a car). You wrap your hand around and twist the rod. The only way the system can move forward, as a lever with fulcrum at the ground, is if the net force is perpendicular to the rotation axis and to the radial axis, and in the forward direction. How does this twisting effect produce such a force? Very confusing to me, these details, since the ground reaction force is right at the fulcrum. Any thought experiments which might help me?

 

[SteamKing]

The axle is rigidly bolted to the wheel. Any torque applied to the axle is going to turn the axle and the wheel together. The turning of the wheel is resisted by the effect of friction between the ground and the wheel. Because of this resistance to the turning of the wheel, the axle and the wheel will then roll along the ground. If there were no friction between the wheel and ground, then the application of torque to the axle would cause both to spin fruitlessly.

To confirm this effect, I urge you to procure a wind-up toy car and perform careful observations and experiments of this effect.

 

[BrainSalad]

Of course this is true. Could the acceleration due to the friction force be viewed as a cancellation of negative momentum in the wheel? For instance, if torque were applied to the axle, causing the system to turn freely, and then the system were dropped to the ground, would the ground force cancel some backward momentum, making net momentum positive (pushing the system forward)?

 

[SteamKing]

Strictly speaking, the friction force is not accelerating the wheel and axle. Friction acts in the direction opposite of motion.

 

[BrainSalad]

Right. I meant to say the ground reaction force.

 

[SteamKing]

Of course this is true. Could the acceleration due to the friction force be viewed as a cancellation of negative momentum in the wheel? For instance, if torque were applied to the axle, causing the system to turn freely, and then the system were dropped to the ground, would the ground force cancel some backward momentum, making net momentum positive (pushing the system forward)?

What backward momentum are you talking about?

 

[BrainSalad]

If the wheel and axle turn freely without forward movement and then the ground force is introduced, the momentum of the bottom of the wheel is changed, but the top part continues forward.

 

[SteamKing]

Yes, but I don't see how that is 'backward momentum'.

 

[BrainSalad]

Haha, negative if you prefer. Taking the forward direction as positive. So I assume the same sort of thing occurs when a torque is applied to the axle as it rests on the ground. The wheels try to turn freely, but their bottom parts are kept stationary, resulting in net forward (positive) momentum due to unrestricted upper portions. The wheel and axle system is a reservoir of momentum, accessed by the ground force cancelling momentum in the negative direction.