Designing a Car for Coasting Race: Wheels

[lo31415926535]

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!

 

[Simon Bridge]

How does the moment of inertial of the wheels contribute to the performance of the car?
Could this be related to your other question?
https://www.physicsforums.com/showthread.php?t=647501

 

[lo31415926535]

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?

 

[Simon Bridge]

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?

 

[lo31415926535]

hmm the one with the small inertia?

 

[Simon Bridge]

Do the free body diagram for sliding down a slope angle $\theta$ to the horizontal.

 

[lo31415926535]

okay so F_N=mgcosθ and ma=mgsinθ

 

[Simon Bridge]

... so which mass reaches the bottom first?

 

[lo31415926535]

they reach the bottom at the same time?

 

[Simon Bridge]

... 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.