UN Fisika 2016 Paket 3 Nomor 14

Perhatikan gambar!

14

Empat partikel yang massanya berbeda terletak sebidang dengan posisi seperti gambar. Momen inersia sistem dengan poros garis mendatar p adalah …

A.        17~m{{b}^{2}} D. 31~m{{b}^{2}}
B.         22~m{{b}^{2}} E. 33~m{{b}^{2}}
C.         27~m{{b}^{2}}

Penyelesaian

Momen inersia I=m{{r}^{2}}

Momen inersia dipengaruhi oleh titik yang tegak lurus poros. Titik yang berada di poros, momen inersianya 0.

 

Momen inersia total \text{ }\!\!\Sigma\!\!\text{ }I=\text{ }\!\!\Sigma\!\!\text{ }m{{r}^{2}}

 

\text{ }\!\!\Sigma\!\!\text{ }I={{m}_{A}}r_{A}^{2}+{{m}_{B}}r_{B}^{2}+{{m}_{C}}r_{C}^{2}+{{m}_{D}}r_{D}^{2}

\text{ }\!\!\Sigma\!\!\text{ }I=m{{(b)}^{2}}+2m{{\left( b \right)}^{2}}+3m{{\left( 2b \right)}^{2}}+4m{{\left( 2b \right)}^{2}}

\text{ }\!\!\Sigma\!\!\text{ }I=m{{b}_{2}}+2m{{b}^{2}}+12m{{b}^{2}}+16m{{b}^{2}}

\text{ }\!\!\Sigma\!\!\text{ }I=31m{{b}^{2}}

jawaban D

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