Supiyanto Kelas X Evaluasi Bab 3 Nomor 9

Roda A dan B sepusat dan keduanya melekat satu sama lain. Roda B dan C dihubungkan dengan tali karet. Jari-jari roda A, B, dan C masing-masing 40 cm, 20 cm, 30 cm. tiap menit roda C berputar 30 kali. Kecepatan tangensial roda A adalah …

A. 30 \text{ }\!\!\pi\!\!\text{  }\!\!~\!\!\text{ cm}/\text{s} D. 60 \text{ }\!\!\pi\!\!\text{  }\!\!~\!\!\text{ cm}/\text{s}
B. 40 \text{ }\!\!\pi\!\!\text{  }\!\!~\!\!\text{ cm}/\text{s} E. 70 \text{ }\!\!\pi\!\!\text{  }\!\!~\!\!\text{ cm}/\text{s}
C. 50 \text{ }\!\!\pi\!\!\text{  }\!\!~\!\!\text{ cm}/\text{s}

Penyelesaian

Jika digambar

9 kunci.gif

Perbandingan kecepatan tangensial B dan C

{{\text{v}}_{\text{B}}}={{\text{v}}_{\text{C}}}

{{\text{ }\!\!\omega\!\!\text{ }}_{\text{B}}}.{{\text{R}}_{\text{B}}}={{\text{ }\!\!\omega\!\!\text{ }}_{\text{C}}}.{{\text{R}}_{\text{C}}}

{{\text{ }\!\!\omega\!\!\text{ }}_{\text{B}}}=\frac{{{\text{ }\!\!\omega\!\!\text{ }}_{\text{C}}}.{{\text{R}}_{\text{C}}}}{{{\text{R}}_{\text{B}}}}=30\frac{\text{putaran}}{\text{menit}}\times \frac{30\text{ }\!\!~\!\!\text{ cm}}{20\text{ }\!\!~\!\!\text{ cm}}=45\frac{\text{putaran}}{\text{menit}}

 

Kecepatan sudut A = kecepatan sudut B

{{\text{ }\!\!\omega\!\!\text{ }}_{\text{A}}}={{\text{ }\!\!\omega\!\!\text{ }}_{\text{B}}}

\frac{{{\text{v}}_{\text{A}}}}{{{\text{R}}_{\text{A}}}}=45\frac{\text{putaran}}{\text{menit}}

{{\text{v}}_{\text{A}}}=45\frac{\text{putaran}}{\text{menit}}\times 40\text{ }\!\!~\!\!\text{ cm}=1800\text{ }\!\!~\!\!\text{ }\frac{\text{putaran}.\text{cm}}{\text{menit}}

 

Konversi ke radian

{{\text{v}}_{\text{A}}}=1800\text{ }\!\!~\!\!\text{ }\frac{\text{putaran}.\text{cm}}{\text{menit}}=1800\times 2\text{ }\!\!\pi\!\!\text{  }\!\!~\!\!\text{ }\frac{\text{rad}.\text{cm}}{60\text{ }\!\!~\!\!\text{ detik }\!\!~\!\!\text{ }}=60\text{ }\!\!\pi\!\!\text{  }\!\!~\!\!\text{ rad}.\frac{\text{cm}}{\text{s}}=60\text{ }\!\!\pi\!\!\text{  }\!\!~\!\!\text{ cm}/\text{s}

 

n.b:

  • Satuan radian boleh ditulis, boleh juga tidak ditulis dalam satuan karena tidak memiliki dimensi
  • 1 putaran = 2\text{ }\!\!\pi\!\!\text{ }\!\!~\!\!\text{ rad}=360{}^\circ

 

Jawaban D

Supiyanto. 2006. FISIKA UNTUK SMA KELAS X. Jakarta: Phiβeta.

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