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Moment of Inertia?

  1. Oct 27, 2012 #1
    1. The problem statement, all variables and given/known data

    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.)

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

    3. 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!
     
  2. jcsd
  3. Oct 27, 2012 #2

    Simon Bridge

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  4. Oct 27, 2012 #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?
     
  5. Oct 27, 2012 #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?
     
  6. Oct 27, 2012 #5
    hmm the one with the small inertia?
     
  7. Oct 28, 2012 #6

    Simon Bridge

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    Do the free body diagram for sliding down a slope angle ##\theta## to the horizontal.
     
  8. Oct 28, 2012 #7
    okay so FN=mgcosθ and ma=mgsinθ
     
  9. Oct 28, 2012 #8

    Simon Bridge

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    ... so which mass reaches the bottom first?
     
  10. Oct 28, 2012 #9
    they reach the bottom at the same time?
     
  11. Oct 28, 2012 #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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