Designing a Car for Coasting Race: Wheels

AI Thread Summary
When designing a car for a coasting race, the choice of wheel size and type significantly impacts performance. Smaller, lighter wheels with a solid, disk-like structure are suggested to reduce the moment of inertia, which theoretically allows for quicker motion. However, the discussion reveals that while lower moment of inertia reduces resistance, it does not directly correlate with faster speeds in a coasting scenario, as all objects experience the same gravitational force and acceleration on a slope. The conversation also emphasizes the importance of understanding the dynamics of rolling versus sliding objects to determine the best wheel design. Ultimately, the relationship between wheel characteristics and car performance is complex and requires careful consideration of both inertia and the physics of motion.
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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!
 
Physics news on Phys.org
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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