Moment of Inertia?

  • #1

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!
 

Answers and Replies

  • #3
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?
 
  • #4
Simon Bridge
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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?
 
  • #5
hmm the one with the small inertia?
 
  • #6
Simon Bridge
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Do the free body diagram for sliding down a slope angle ##\theta## to the horizontal.
 
  • #7
okay so FN=mgcosθ and ma=mgsinθ
 
  • #8
Simon Bridge
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... so which mass reaches the bottom first?
 
  • #9
they reach the bottom at the same time?
 
  • #10
Simon Bridge
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... 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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