(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A driver starts his car with the door on the passenger’s side

wide open ([tex]\omega[/tex] = 0) the 36-kg door has a centroidal radius of gyration

k= 250 mm, and its mass center is located at a distance r = 440 mm from

its vertical axis of rotation. Knowing that the driver maintains a constant

acceleration of 2 m/s^{2}, determine the angular velocity of the door as it

slams shut ([tex]\omega[/tex] = 90°).

R = 440mm = .44m

k = 250mm = .25m

a = 2 m/s

m = 36kg

2. Relevant equations

[tex]\Sigma[/tex]M = I_{g}[tex]\alpha[/tex] + [tex]\Sigma[/tex] r x ma_{g}... (1)

[tex]\omega[/tex] = [tex]\omega[/tex]_{0}+ 2[tex]\alpha[/tex][tex]\theta[/tex]

a = R[tex]\alpha[/tex]

3. The attempt at a solution

[tex]\Sigma[/tex]M = I_{g}[tex]\alpha[/tex] + [tex]\Sigma[/tex] r x ma_{g}

::: [tex]\Sigma[/tex]M = W_{g}R cos([tex]\theta[/tex])

* even though i did this...what do i use for theta? (90? degrees)

* also, i think the only thing that contributes to the moment is the weight of the door?

::: I_{g}[tex]\alpha[/tex] + [tex]\Sigma[/tex] r x ma_{g}

= I[tex]\alpha[/tex] + maR

= mk^{2}[tex]\alpha[/tex] + mR^{2}[tex]\alpha[/tex]

after i complete (1) i get this when i solve for alpha:

[tex]\alpha[/tex] = Rg/ (k^{2}+ R^{2}cos([tex]\theta[/tex])

and then i get stuck here. i didn't know what to use for the theta, but i think im suppose to find [tex]\alpha[/tex] and then use the kinematic equation:

[tex]\omega[/tex] = [tex]\omega[/tex]_{0}+ 2[tex]\alpha[/tex][tex]\theta[/tex]

a = R[tex]\alpha[/tex]

to find omega, and i know omega initial = 0 ??

i feel like im missing an important part of the equation because im not getting the right answer...and i don't quite understand it. Im a little confused on the cosine part, am i suppose to use that for the acceleration, and not the moment of the weight? if someone can please help?!? i would appreciate it!! Thanks!! :D :D

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# Homework Help: Moment of inertia car problem

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