Mechanics of Wheel and Forces Involved

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SUMMARY

The discussion focuses on the mechanics of wheel dynamics, specifically the forces acting on a wheel when subjected to tractive effort E and braking forces. It confirms that the tractive effort can be resolved into a couple and a forward force at the contact point with the surface. Additionally, it addresses the role of limiting friction force F, which acts against the direction of motion, and clarifies that if the tractive effort exceeds this friction force, wheel slip occurs. The participants also explore the calculation of deceleration when a braking force is applied to a weightless wheel with mass M.

PREREQUISITES
  • Understanding of basic physics concepts related to forces and motion.
  • Familiarity with the principles of friction, particularly limiting friction.
  • Knowledge of wheel dynamics and the role of tractive effort in motion.
  • Basic mathematical skills for resolving forces and calculating deceleration.
NEXT STEPS
  • Study the principles of limiting friction and its impact on wheel slip.
  • Learn about the equations of motion and how they apply to rotating bodies.
  • Explore the dynamics of braking systems in bicycles and vehicles.
  • Investigate the effects of weight and moment of inertia on wheel performance.
USEFUL FOR

This discussion is beneficial for mechanical engineers, physics students, and anyone interested in understanding the dynamics of wheels and braking systems in vehicles and bicycles.

Eugbug
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If an axle is being pulled with a tractive effort E, can this be resolved into a couple and forwards force E at the point of contact with a surface? Is it correct to add a limiting friction force F acting backwards against the direction of motion and if this is exceeded by E, does the wheel slip?
 

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Hi Eugbug! :smile:
Eugbug said:
If an axle is being pulled with a tractive effort E, can this be resolved into a couple and forwards force E at the point of contact with a surface?

Yes, that's completely correct …

the two alternative descriptions are completely equivalent. :smile:​

But I don't see how that helps you with the friction force :confused: …
Is it correct to add a limiting friction force F acting backwards against the direction of motion and if this is exceeded by E, does the wheel slip?
 
The inspiration for this question came about when I was coming down a mountain at top speed on my mountain bike and was thinking about how braking works on a wheel and whether a skid can occur if enough braking force is applied and the wheels don't actually lock.
To make things simple, take a single wheel rolling along a level surface. The wheel is weightless so there is no moment of inertia to take into account, just say there is a mass M attached to the axle. If a braking force is applied at the perimeter of the wheel and this produces a sliding friction force Fb acting against the direction of rotation of the wheel, what are the forces involved and how do you work out the deceleration of the wheel? The velocity of the wheel is v.

The way I would approach things is to resolve Fb into a couple Fb and a force Fb acting against the direction of motion at the axle and then the equation of motion becomes:

-Fb = Ma where a is the deceleration of the wheel. Is this correct?
 

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