Designing a Car for Coasting Race: Wheels

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SUMMARY

The discussion centers on the design considerations for wheels in a coasting race car, specifically the impact of wheel size, shape, and weight on performance. The key factors include the moment of inertia, defined by the equations for hoop-like wheels (I=MR²) and solid cylinders (I=(1/2)MR²). A lower moment of inertia reduces resistance to motion, allowing for quicker acceleration. The conclusion drawn is that while smaller, lighter wheels may seem advantageous, the actual performance is influenced by the dynamics of rolling objects, which requires further analysis of forces and accelerations.

PREREQUISITES
  • Understanding of moments of inertia for different shapes (hoop vs. solid cylinder)
  • Basic principles of physics related to motion and acceleration
  • Familiarity with free body diagrams and forces acting on objects
  • Knowledge of linear inertia and its relationship with mass
NEXT STEPS
  • Research the effects of wheel size on rolling resistance and acceleration
  • Study the relationship between moment of inertia and angular acceleration
  • Explore the dynamics of rolling objects on inclined planes
  • Investigate the principles of energy conservation in coasting scenarios
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in the dynamics of rolling motion and vehicle design for coasting races.

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Homework Statement



Suppose you are designing a car for a coasting race -- the cars in this race have no engines, they simply coast down a hill. Do you want large wheels or small wheels? Do you want solid, disk-like wheels, or hoop-like wheels? Should be wheels be heavy or light? (Select all that apply. Omit both choices in a pair if neither have a beneficial effect.)

Homework Equations


Moments of Inertia:
Hoop or thin cylindrical shell:
I=MR2
Solid cylinder:
I=(1/2)MR2

The Attempt at a Solution



The options are:

large
small
solid, disk-like
hoop-like
heavy
light

So I guessed small; solid, disk-like; and light because according to those equations above, those options would make it have a lower moment of inertia… but according to webassign, that is wrong, and I do not understand why. Can someone help?

Thank you in advance!
 
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Well a lower moment of inertia would mean less resistance to motion right? so it would move more quickly? and yes this is related to the other question… Am I approaching it right by using moment of inertia?
 
Linear inertia = mass.
You have a race between two blocks mass M and m with M>m sliding down a frictionless slope. Which one reaches the bottom first: the one with the big inertia or the one with the small inertia?
 
hmm the one with the small inertia?
 
Do the free body diagram for sliding down a slope angle ##\theta## to the horizontal.
 
okay so FN=mgcosθ and ma=mgsinθ
 
... so which mass reaches the bottom first?
 
they reach the bottom at the same time?
 
  • #10
... since they experience the same force, they have the same acceleration, their inertia does not matter.

Now you need something similar for an object rolling: which is where that other thread comes in. Answer that and you'll have this answer as well.
 

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