Sahabat fisioner kali ini kita akan membahas topik tentang hukum kekekalan momentum sudut dan aplikasinya pada penari balet. Terdapat beberapa penerapan hukum kekekalan momentum sudut dalam kehidupan kita, misalnya penari balet, atlet ice skating, atlet loncat indah, dan yang lainnya. Sudah tahukah sahabat fisioner dengan hukum kekekalan momentum sudut? Untuk lebih memahaminya silahkan sahabat fisioner mempelajari topik tentang hukum kekekalan momentum sudut dan aplikasinya pada penari balet berikut ini.
Topik: Hukum kekekalan momentum sudut dan aplikasinya pada penari balet
1. Konsep hukum kekekalan momentum
Momentum Sudut
Anda telah mengenal besaran momentum linear yang dinyatakan oleh P = m.v. Pada gerak rotasi, yang analog dengan momentum linear adalah momentum sudut. Massa analog dengan momen inersia, kecepatan linear analog dengan kecepatan sudut, maka momentum sudut momentum sudut didefinisikan sebagai perkalian antara momen inersia dan kecepatan sudut. Secara matematis, ditulis sebagai berikut.
Momentum sudut merupakan besaran vektor karena memiliki besar dan arah. Arah momentum sudut dapat ditentukan dengan aturan tangan kanan, seperti yang ditunjukkan pada Gambar di atas. Arah putaran keempat jari menunjukkan arah rotasi, sedangkan ibu jari menunjukkan arah momentum sudut. Jika lengan torsi terhadap poros r dan kecepatan linear v benda (benda dianggap partikel) diberikan, besar momentum sudut L dapat dihitung sebagai berikut.
Formulasi Hukum Kekekalan Momentum Sudut pada Gerak Rotasi
Hukum kekekalan momentum linear menyatakan bahwa jika pada suatu sistem tidak bekerja resultan gaya luar (SF =
0 ), momentum linear sistem adalah kekal (tetap besarnya). Pada gerak rotasi pun anda akan menjumpai hukum kekekalan momentum sudut. Jika momen gaya luar sama dengan nol, berlaku Hukum Kekekalan Momentum Sudut, yaitu momentum sudut awal akan sama besar dengan momentum sudut akhir. Secara matematis, pernyataan tersebut ditulis sebagai berikut.
Hukum Kekekalan momentum sudut
“ jika tidak ada resultan momen gaya luar yang bekerja pada sistem (St = 0), momentum sudut sistem adalah kekal (tetap besarnya)”.
Dari persamaan hukum kekekalan momentum sudut, dapat dilihat bahwa apabila I bertambah besar, ω akan semakin kecil. Sebaliknya, apabila ω semakin besar maka I akan mengecil.
2. Contoh Soal
Seorang penari balet memiliki
momen inersia 8 kgm2 ketika kedua lengannya terlentang dan 2 kgm2
ketika merapat ke tubuhnya. Pada saat kedua lengannya terlentang, penari
tersebut berputar dengan kelajuan 3 putaran/s. Setelah itu, kedua lengannya
dirapatkan ke tubuhnya. Tentukanlah laju putaran penari ketika kedua lengannya
merapat!
Penyelesaian
Diketahui:
I = 8 kgm2
I’= 2 kg m2
ω = 3 putaran/s
Ditanyakan : ω ' = ...?
Jawab:
Jadi lajunya adalah 12 putaran/s.
3. Aplikasi hukum kekekalan momentum sudut pada penari balet
Terdapat beberapa penerapan hukum kekekalan momentum sudut dalam kehidupan kita, misalnya pada penari balet. Penari balet dalam melakukan putaran mengaplikasikan hukum kekekalan momentum. Saat akan memulai putaran badan, penari balet merentangkan lengannya (momen inersia penari akan semakin besar karena jarak lengan dengan badan bertambah). Kemudian, ia merapatkan kedua lengannya ke arah atas badannya agar momen inersianya mengecil (karena jarak lengan dengan badan mengecil) sehingga putaran badannya akan semakin cepat (kecepatan sudutnya membesar).
Demikianlah penjelasan tentang hukum kekekalan momentum sudut dan aplikasinya pada penari balet. Semoga memberikan wawasan dan memberikan semangat untuk senantiasa belajar fisika.
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