[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"public-settings":3,"content:materi:momen-inersia":11,"public-catalog":193},{"features.tutoring.enabled":4,"sections.subjects.enabled":5,"sections.pricing.enabled":5,"sections.teachers.enabled":5,"sections.testimonials.enabled":4,"sections.faqs.enabled":5,"bankSoal.enabled":5,"site.maintenance":4,"whatsapp.number":6,"brand.name":7,"brand.tagline":8,"contact.email":9,"contact.address":10},false,true,"6285156084435","MyFismat","Platform belajar Matematika, Fisika, dan Pemrograman untuk SD, SMP, SMA, dan Kuliah","support@myfismat.com","Indonesia",{"id":12,"type":13,"slug":14,"title":15,"excerpt":16,"coverUrl":17,"status":18,"publishedAt":19,"featured":4,"subjectId":20,"blocks":21,"seoTitle":17,"seoDescription":17,"readingMinutes":90,"order":91,"createdAt":92,"updatedAt":92,"subject":93,"levels":98,"topics":103,"tags":107,"author":17,"resolved":108,"related":118},"demo-v2-m-fisika-kuliah-3","MATERIAL","momen-inersia","Momen Inersia: Rumus Benda Tegar dan Contoh Soal","Momen inersia benda tegar: rumus I = Σmr² dan ∫r² dm, tabel batang, silinder, bola, teorema sumbu sejajar, energi kinetik rotasi, dan contoh soal.",null,"PUBLISHED","2026-10-08T23:58:23.446Z","cmuzbyhdq000571r9nsdk6scx",[22,27,34,38,42,46,50,54,58,62,66,72,76,80,84],{"id":23,"data":24,"type":26},"s1-1",{"markdown":25},"**Momen inersia** adalah ukuran kelembaman benda terhadap perubahan gerak rotasi di sekitar suatu sumbu. Untuk sistem partikel, $I = \\sum m_i r_i^2$; untuk benda kontinu, $I = \\int r^2\\,dm$, dengan $r$ jarak tegak lurus ke sumbu putar. Satuannya kg·m². Nilainya bergantung pada massa, bentuk benda, dan letak sumbu putar.","text",{"id":28,"data":29,"type":33},"s1-2",{"title":30,"variant":31,"markdown":32},"Rumus momen inersia","info","$$I = \\sum_i m_i r_i^2 \\qquad I = \\int r^2\\,dm$$\n\nTeorema sumbu sejajar: $I = I_{\\text{pm}} + M d^2$.\n\nEnergi kinetik rotasi $K = \\tfrac12 I\\omega^2$ dan hukum Newton 2 rotasi $\\tau = I\\alpha$.","callout",{"id":35,"data":36,"type":26},"s2-1",{"markdown":37},"## Apa Itu Momen Inersia?\n\nPada gerak lurus, massa menyatakan seberapa sulit benda dipercepat. Pada gerak rotasi, peran itu diambil oleh **momen inersia**. Semakin besar momen inersia, semakin besar torsi yang diperlukan untuk mengubah kecepatan sudut benda.\n\nMomen inersia tidak hanya bergantung pada massa, tetapi juga pada **sebaran massa terhadap sumbu putar**. Massa yang jauh dari sumbu menyumbang jauh lebih besar karena jaraknya dikuadratkan. Itulah sebabnya pemain seluncur es berputar lebih cepat saat merapatkan lengannya.\n\nJarak $r$ pada rumus adalah jarak **tegak lurus** dari elemen massa ke sumbu putar, bukan jarak ke titik asal koordinat. Benda yang sama dapat mempunyai momen inersia berbeda untuk sumbu yang berbeda.",{"id":39,"data":40,"type":26},"s3-1",{"markdown":41},"## Rumus Momen Inersia Sistem Partikel\n\nUntuk beberapa partikel titik, jumlahkan $m r^2$ setiap partikel: $I = m_1 r_1^2 + m_2 r_2^2 + \\dots$ Satuannya kg·m². Batang penghubung yang sangat ringan dapat diabaikan.",{"id":43,"data":44,"type":26},"s4-1",{"markdown":45},"## Menghitung Momen Inersia Benda Tegar dengan Integral\n\nUntuk benda kontinu, ganti penjumlahan dengan integral $I = \\int r^2\\,dm$. Kuncinya adalah menyatakan $dm$ dengan variabel posisi.\n\n**Batang homogen** bermassa $M$ dan panjang $L$ memiliki rapat massa linear $\\lambda = M\u002FL$, sehingga $dm = \\lambda\\,dx$. Terhadap sumbu yang tegak lurus batang dan melalui pusatnya:\n\n$$I_{\\text{pm}} = \\int_{-L\u002F2}^{L\u002F2} x^2\\,\\lambda\\,dx = \\lambda\\left[\\frac{x^3}{3}\\right]_{-L\u002F2}^{L\u002F2} = \\frac{1}{12}ML^2$$\n\nTerhadap sumbu di salah satu ujung, batas integralnya 0 sampai $L$:\n\n$$I_{\\text{ujung}} = \\int_0^L x^2\\,\\lambda\\,dx = \\frac{1}{3}ML^2$$\n\nUntuk **cincin tipis** terhadap sumbu simetrinya, semua massa berjarak $R$ dari sumbu, sehingga langsung $I = MR^2$.",{"id":47,"data":48,"type":26},"s5-1",{"markdown":49},"## Tabel Rumus Momen Inersia Benda Tegar\n\n| Benda (homogen) | Sumbu putar | Momen inersia |\n|---|---|---|\n| Batang tipis | Melalui pusat, tegak lurus batang | $\\tfrac{1}{12}ML^2$ |\n| Batang tipis | Melalui ujung, tegak lurus batang | $\\tfrac13 ML^2$ |\n| Cincin tipis atau silinder berongga tipis | Sumbu simetri | $MR^2$ |\n| Piringan atau silinder pejal | Sumbu simetri | $\\tfrac12 MR^2$ |\n| Bola pejal | Melalui pusat | $\\tfrac25 MR^2$ |\n| Bola berongga tipis | Melalui pusat | $\\tfrac23 MR^2$ |\n| Pelat persegi panjang $a \\times b$ | Melalui pusat, tegak lurus pelat | $\\tfrac{1}{12}M(a^2 + b^2)$ |",{"id":51,"data":52,"type":26},"s6-1",{"markdown":53},"## Teorema Sumbu Sejajar\n\nJika momen inersia terhadap sumbu yang melalui pusat massa, $I_{\\text{pm}}$, sudah diketahui, momen inersia terhadap sumbu lain yang **sejajar** dan berjarak $d$ adalah $I = I_{\\text{pm}} + Md^2$.\n\nCek untuk batang: $\\tfrac{1}{12}ML^2 + M(L\u002F2)^2 = \\tfrac{1}{12}ML^2 + \\tfrac{3}{12}ML^2 = \\tfrac13 ML^2$, sama dengan hasil integral. Teorema ini hanya berlaku jika salah satu sumbu melalui pusat massa.",{"id":55,"data":56,"type":26},"s7-1",{"markdown":57},"## Energi Kinetik Rotasi dan Hukum Newton 2 Rotasi\n\nBenda yang berputar dengan kecepatan sudut $\\omega$ menyimpan **energi kinetik rotasi** $K = \\tfrac12 I\\omega^2$. Torsi resultan menghasilkan percepatan sudut menurut $\\tau = I\\alpha$, bentuk rotasi dari $\\Sigma F = m\\,a$.\n\nBenda yang **menggelinding tanpa slip** memiliki energi kinetik translasi dan rotasi sekaligus: $K = \\tfrac12 Mv^2 + \\tfrac12 I\\omega^2$, dengan $v = \\omega R$. Karena itu, benda yang momen inersianya relatif kecil, seperti bola pejal, lebih cepat sampai di dasar bidang miring daripada silinder pejal.",{"id":59,"data":60,"type":26},"s8-1",{"markdown":61},"## Contoh Soal Momen Inersia dan Pembahasan\n\n### Contoh 1: sistem dua partikel\n\nPartikel 2 kg dan 3 kg dipasang pada batang ringan, masing-masing berjarak 0,5 m dan 1 m dari sumbu putar. Berapa momen inersia sistem?\n\nPembahasan: $I = 2(0{,}5)^2 + 3(1)^2 = 0{,}5 + 3 = 3{,}5$ kg·m².\n\n### Contoh 2: batang dengan dua sumbu berbeda\n\nBatang homogen bermassa 3 kg dan panjang 1,2 m. Hitung momen inersianya terhadap sumbu di pusat dan di ujung.\n\nPembahasan: di pusat, $I = \\tfrac{1}{12}(3)(1{,}2)^2 = \\tfrac{1}{12}(3)(1{,}44) = 0{,}36$ kg·m². Di ujung, $I = \\tfrac13(3)(1{,}44) = 1{,}44$ kg·m². Cek dengan teorema sumbu sejajar: $0{,}36 + 3(0{,}6)^2 = 0{,}36 + 1{,}08 = 1{,}44$ kg·m².\n\n### Contoh 3: energi dan torsi piringan\n\nPiringan pejal bermassa 2 kg dan berjari-jari 0,3 m berputar 10 rad\u002Fs pada sumbu simetrinya. Berapa energi kinetik rotasinya, dan berapa torsi tetap yang diperlukan untuk menghentikannya dalam 3 s?\n\nPembahasan: $I = \\tfrac12(2)(0{,}3)^2 = 0{,}09$ kg·m² dan $K = \\tfrac12(0{,}09)(10^2) = 4{,}5$ J. Perlambatan sudut $\\alpha = 10\u002F3 \\approx 3{,}33$ rad\u002Fs², sehingga $\\tau = I\\alpha = 0{,}09 \\times 10\u002F3 = 0{,}3$ N·m.\n\n### Contoh 4: bola pejal dan silinder pejal menggelinding\n\nBola pejal dan silinder pejal dilepas dari ketinggian 1 m pada bidang miring dan menggelinding tanpa slip. Dengan $g = 9{,}8$ m\u002Fs², berapa kelajuan masing-masing di dasar?\n\nPembahasan: tulis $I = \\beta MR^2$. Kekekalan energi memberi $Mgh = \\tfrac12 Mv^2(1 + \\beta)$, sehingga $v = \\sqrt{2gh\u002F(1 + \\beta)}$. Bola pejal ($\\beta = 2\u002F5$): $v = \\sqrt{19{,}6\u002F1{,}4} = \\sqrt{14} \\approx 3{,}74$ m\u002Fs. Silinder pejal ($\\beta = 1\u002F2$): $v = \\sqrt{19{,}6\u002F1{,}5} \\approx 3{,}61$ m\u002Fs. Massa dan jari-jari tidak berpengaruh.",{"id":63,"data":64,"type":26},"s9-1",{"markdown":65},"## Kesalahan yang Sering Terjadi",{"id":67,"data":68,"type":33},"s9-2",{"title":69,"variant":70,"markdown":71},"Perhatikan sumbunya","warning","- Memakai jarak ke titik asal, bukan jarak tegak lurus ke sumbu putar.\n- Memakai rumus tabel untuk sumbu yang berbeda, misalnya $\\tfrac{1}{12}ML^2$ untuk batang yang diputar di ujung.\n- Menerapkan teorema sumbu sejajar antara dua sumbu yang keduanya tidak melalui pusat massa.\n- Menyamakan momen inersia dengan momen gaya (torsi). Satuan momen inersia kg·m², sedangkan satuan torsi N·m.",{"id":73,"data":74,"type":26},"s10-1",{"markdown":75},"## Ringkasan\n\n- Momen inersia $I = \\sum m r^2$ atau $\\int r^2\\,dm$, dengan $r$ jarak tegak lurus ke sumbu.\n- Batang: $\\tfrac{1}{12}ML^2$ (pusat) dan $\\tfrac13 ML^2$ (ujung); silinder pejal $\\tfrac12 MR^2$; bola pejal $\\tfrac25 MR^2$.\n- Teorema sumbu sejajar: $I = I_{\\text{pm}} + Md^2$.\n- Energi kinetik rotasi $\\tfrac12 I\\omega^2$ dan $\\tau = I\\alpha$.",{"id":77,"data":78,"type":26},"s11-1",{"markdown":79},"## Materi Terkait\n\n- [Hukum Newton 2](\u002Fmateri\u002Fhukum-newton-2): versi translasi dari $\\tau = I\\alpha$.\n- [Usaha oleh Gaya Berubah](\u002Fmateri\u002Fusaha-oleh-gaya-berubah): teorema usaha–energi yang juga berlaku pada rotasi.\n- [Gerak Harmonik Sederhana](\u002Fmateri\u002Fgerak-harmonik-sederhana): osilasi yang juga muncul pada bandul fisis.\n- Lihat semua materi di [halaman mapel Fisika](\u002Fmapel\u002Ffisika).",{"id":81,"data":82,"type":26},"sources",{"markdown":83},"## Sumber belajar\n\n- [OpenStax University Physics Volume 1 — Moment of Inertia and Rotational Kinetic Energy](https:\u002F\u002Fopenstax.org\u002Fbooks\u002Funiversity-physics-volume-1\u002Fpages\u002F10-4-moment-of-inertia-and-rotational-kinetic-energy)\n- [OpenStax University Physics Volume 1 — Calculating Moments of Inertia](https:\u002F\u002Fopenstax.org\u002Fbooks\u002Funiversity-physics-volume-1\u002Fpages\u002F10-5-calculating-moments-of-inertia)\n- [Wikipedia bahasa Indonesia — Momen inersia](https:\u002F\u002Fid.wikipedia.org\u002Fwiki\u002FMomen_inersia)\n\nPenjelasan dan contoh disusun ulang untuk materi ini; sumber dapat dibuka untuk belajar lebih lanjut.",{"id":85,"data":86,"type":89},"practice",{"title":87,"questionSetId":88},"Latihan soal Momen 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soal.","2026-10-08T23:58:23.416Z",6,1,"2026-10-08T23:58:23.418Z",{"id":20,"slug":94,"name":95,"color":96,"icon":97},[157],{"id":100,"slug":101,"name":102},[159],{"id":160,"slug":148,"name":161,"subjectId":20},"demo-v2-topic-fisika-kuliah-2","Usaha Gaya Berubah",[],{"id":164,"type":13,"slug":165,"title":166,"excerpt":167,"coverUrl":17,"status":18,"publishedAt":168,"featured":5,"readingMinutes":152,"order":127,"updatedAt":169,"subject":170,"levels":171,"topics":173,"tags":177,"author":17},"demo-v2-m-fisika-kuliah-1","gerak-harmonik-sederhana","Gerak Harmonik Sederhana: Rumus Simpangan, Periode, Energi","Gerak harmonik sederhana untuk fisika dasar: persamaan x = A cos(ωt + φ), kecepatan, percepatan, periode pegas dan bandul, energi, serta contoh soal.","2026-10-08T23:58:23.386Z","2026-10-08T23:58:23.388Z",{"id":20,"slug":94,"name":95,"color":96,"icon":97},[172],{"id":100,"slug":101,"name":102},[174],{"id":175,"slug":165,"name":176,"subjectId":20},"demo-v2-topic-fisika-kuliah-1","Gerak 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12.","2026-10-08T09:24:41.215Z",{"id":397,"subjectId":20,"levelId":140,"parentId":17,"slug":1713,"name":1714,"description":1715,"order":1716,"createdAt":1717,"updatedAt":1717},"listrik-arus-searah","Listrik Arus Searah","Listrik Arus Searah — Kelas 12.",23,"2026-10-08T09:24:41.227Z",{"id":445,"subjectId":196,"levelId":140,"parentId":17,"slug":1719,"name":1568,"description":1720,"order":1716,"createdAt":1721,"updatedAt":1721},"peluang-kelas-12-wajib","Peluang — Kelas 12 Wajib.","2026-10-08T09:24:41.547Z",{"id":409,"subjectId":196,"levelId":140,"parentId":17,"slug":1723,"name":1724,"description":1725,"order":1726,"createdAt":1727,"updatedAt":1727},"geometri-analitik","Geometri Analitik","Geometri Analitik — Kelas 12 Lanjut.",24,"2026-10-08T09:24:41.553Z",{"id":403,"subjectId":20,"levelId":140,"parentId":17,"slug":1729,"name":1730,"description":1731,"order":1726,"createdAt":1732,"updatedAt":1732},"kemagnetan","Kemagnetan","Kemagnetan — Kelas 12.","2026-10-08T09:24:41.245Z",{"id":277,"subjectId":196,"levelId":140,"parentId":17,"slug":1734,"name":1735,"description":1736,"order":1737,"createdAt":1738,"updatedAt":1738},"limit","Limit","Limit — Kelas 12 Lanjut.",25,"2026-10-08T09:24:41.562Z",{"id":229,"subjectId":20,"levelId":140,"parentId":17,"slug":1740,"name":1741,"description":1742,"order":1737,"createdAt":1743,"updatedAt":1743},"listrik-ac-arus-bolak-balik","Listrik AC \u002F Arus Bolak Balik","Listrik AC \u002F Arus Bolak Balik — Kelas 12.","2026-10-08T09:24:41.263Z",{"id":468,"subjectId":20,"levelId":140,"parentId":17,"slug":1745,"name":1746,"description":1747,"order":1748,"createdAt":1749,"updatedAt":1749},"gelombang-elektromagnetik","Gelombang Elektromagnetik","Gelombang Elektromagnetik — Kelas 12.",26,"2026-10-08T09:24:41.273Z",{"id":283,"subjectId":196,"levelId":140,"parentId":17,"slug":1751,"name":1752,"description":1753,"order":1748,"createdAt":1754,"updatedAt":1754},"turunan-fungsi","Turunan Fungsi","Turunan Fungsi — Kelas 12 Lanjut.","2026-10-08T09:24:41.575Z",{"id":492,"subjectId":196,"levelId":140,"parentId":17,"slug":1756,"name":1757,"description":1758,"order":1759,"createdAt":1760,"updatedAt":1760},"aplikasi-turunan","Aplikasi Turunan","Aplikasi Turunan — Kelas 12 Lanjut.",27,"2026-10-08T09:24:41.587Z",{"id":522,"subjectId":20,"levelId":140,"parentId":17,"slug":1762,"name":1763,"description":1764,"order":1759,"createdAt":1765,"updatedAt":1765},"pengantar-instrumental-digital","Pengantar Instrumental Digital","Pengantar Instrumental Digital — Kelas 12.","2026-10-08T09:24:41.283Z",{"id":367,"subjectId":196,"levelId":140,"parentId":17,"slug":1767,"name":1768,"description":1769,"order":1770,"createdAt":1771,"updatedAt":1771},"integral","Integral","Integral — Kelas 12 Lanjut.",28,"2026-10-08T09:24:41.599Z",{"id":510,"subjectId":20,"levelId":140,"parentId":17,"slug":1773,"name":1774,"description":1775,"order":1770,"createdAt":1776,"updatedAt":1776},"relativitas-khusus","Relativitas Khusus","Relativitas Khusus — Kelas 12.","2026-10-08T09:24:41.291Z",{"id":516,"subjectId":20,"levelId":140,"parentId":17,"slug":1778,"name":1779,"description":1780,"order":1781,"createdAt":1782,"updatedAt":1782},"gejala-kuantum","Gejala Kuantum","Gejala Kuantum — Kelas 12.",29,"2026-10-08T09:24:41.303Z",{"id":415,"subjectId":196,"levelId":140,"parentId":17,"slug":1784,"name":1785,"description":1786,"order":1781,"createdAt":1787,"updatedAt":1787},"penerapan-integral","Penerapan Integral","Penerapan Integral — Kelas 12 Lanjut.","2026-10-08T09:24:41.607Z",{"id":307,"subjectId":196,"levelId":140,"parentId":17,"slug":1789,"name":1790,"description":1791,"order":1792,"createdAt":1793,"updatedAt":1793},"analisis-data-peluang","Analisis Data & Peluang","Analisis Data & Peluang — Kelas 12 Lanjut.",30,"2026-10-08T09:24:41.611Z",{"id":451,"subjectId":20,"levelId":140,"parentId":17,"slug":1795,"name":1796,"description":1797,"order":1792,"createdAt":1798,"updatedAt":1798},"fisika-inti-dan-radioaktivitas","Fisika Inti dan Radioaktivitas","Fisika Inti dan Radioaktivitas — Kelas 12.","2026-10-08T09:24:41.318Z",{"id":1800,"subjectId":196,"levelId":140,"parentId":17,"slug":1801,"name":1802,"description":1803,"order":1804,"createdAt":1805,"updatedAt":1805},"cmuzbyhw700gw71r9o87lq7vd","logaritma","Logaritma","Logaritma — Kelas 12 Lanjut.",31,"2026-10-08T09:24:41.623Z",{"id":1807,"subjectId":196,"levelId":140,"parentId":17,"slug":1808,"name":1809,"description":1810,"order":1811,"createdAt":1812,"updatedAt":1812},"cmuzbyhw900gy71r9d9sjh9ie","program-linier","Program Linier","Program Linier — Kelas 12 Lanjut.",32,"2026-10-08T09:24:41.625Z",{"id":1814,"subjectId":196,"levelId":140,"parentId":17,"slug":1815,"name":1816,"description":1817,"order":1818,"createdAt":1819,"updatedAt":1819},"cmuzbyhwb00h071r97764r7hr","bangun-ruang","Bangun Ruang","Bangun Ruang — Kelas 12 Lanjut.",33,"2026-10-08T09:24:41.627Z",{"id":1821,"subjectId":196,"levelId":100,"parentId":17,"slug":1822,"name":285,"description":1823,"order":1824,"createdAt":1825,"updatedAt":1825},"demo-v2-topic-matematika-kuliah-1","definisi-turunan-limit","Definisi turunan dengan limit f′(x) = lim [f(x+h) − f(x)]\u002Fh, langkah menghitungnya, gradien garis singgung, syarat diferensiabel, dan contoh soal.",100,"2026-10-08T23:58:22.977Z",{"id":1827,"subjectId":196,"levelId":140,"parentId":17,"slug":1828,"name":1829,"description":1830,"order":1824,"createdAt":1831,"updatedAt":1831},"demo-v2-topic-matematika-sma-1","fungsi-kuadrat","Fungsi Kuadrat","Fungsi kuadrat f(x) = ax² + bx + c: pengaruh a, b, c pada grafik, rumus titik puncak, sumbu simetri, diskriminan, dan contoh soal nilai maksimum.","2026-10-08T23:58:22.868Z",{"id":1833,"subjectId":207,"levelId":140,"parentId":17,"slug":1834,"name":1835,"description":1836,"order":1824,"createdAt":1837,"updatedAt":1837},"demo-v2-topic-pemrograman-sma-1","fungsi-python-def-return","Fungsi Python","Pelajari cara membuat fungsi Python dengan def, parameter, nilai default, dan return, plus perbedaan return dan print lewat contoh program yang jelas.","2026-10-08T23:58:23.661Z",{"id":1839,"subjectId":20,"levelId":136,"parentId":17,"slug":1840,"name":1841,"description":1842,"order":1824,"createdAt":1843,"updatedAt":1843},"demo-v2-topic-fisika-smp-1","glb-dan-glbb","GLB dan GLBB","Rumus GLB dan GLBB lengkap: jarak, kecepatan, percepatan, grafik posisi–waktu, perbedaan GLB dan GLBB, plus contoh soal gerak lurus dan pembahasannya.","2026-10-08T23:58:23.189Z",{"id":175,"subjectId":20,"levelId":100,"parentId":17,"slug":165,"name":176,"description":167,"order":1824,"createdAt":1845,"updatedAt":1845},"2026-10-08T23:58:23.364Z",{"id":1847,"subjectId":20,"levelId":140,"parentId":17,"slug":1848,"name":1849,"description":1850,"order":1824,"createdAt":1851,"updatedAt":1851},"demo-v2-topic-fisika-sma-1","hukum-newton-2","Hukum Newton 2","Hukum Newton 2: bunyi, rumus ΣF = m·a, diagram gaya, gaya gesek statis dan kinetis, serta contoh soal mencari percepatan dan massa beserta pembahasan.","2026-10-08T23:58:23.280Z",{"id":1853,"subjectId":207,"levelId":100,"parentId":17,"slug":1854,"name":1855,"description":1856,"order":1824,"createdAt":1857,"updatedAt":1857},"demo-v2-topic-pemrograman-kuliah-1","notasi-big-o-kompleksitas-waktu","Notasi Big O","Pahami notasi Big O dan kompleksitas waktu algoritma: O(1), O(log n), O(n), O(n²), cara menghitungnya dari kode Python, dan contoh soalnya.","2026-10-08T23:58:23.797Z",{"id":1859,"subjectId":207,"levelId":132,"parentId":17,"slug":1860,"name":1861,"description":1862,"order":1824,"createdAt":1863,"updatedAt":1863},"demo-v2-topic-pemrograman-sd-1","pengertian-algoritma","Pengertian Algoritma","Algoritma adalah langkah-langkah urut untuk menyelesaikan masalah. Pelajari pengertian, ciri, dan contoh algoritma sehari-hari untuk siswa SD.","2026-10-08T23:58:23.477Z",{"id":1865,"subjectId":20,"levelId":132,"parentId":17,"slug":1866,"name":1867,"description":1868,"order":1824,"createdAt":1869,"updatedAt":1869},"demo-v2-topic-fisika-sd-1","pengukuran-panjang","Pengukuran Panjang","Belajar pengukuran panjang untuk SD: satuan baku, alat ukur panjang, cara memakai penggaris, dan tangga satuan panjang km sampai mm + contoh soal.","2026-10-08T23:58:23.095Z",{"id":1871,"subjectId":196,"levelId":132,"parentId":17,"slug":1872,"name":1873,"description":1874,"order":1824,"createdAt":1875,"updatedAt":1875},"demo-v2-topic-matematika-sd-1","penjumlahan-pecahan","Penjumlahan Pecahan","Cara penjumlahan pecahan berpenyebut sama dan beda penyebut memakai KPK, pecahan senilai, dan pecahan campuran, lengkap dengan contoh soal SD.","2026-10-08T23:58:22.508Z",{"id":1877,"subjectId":196,"levelId":136,"parentId":17,"slug":1878,"name":1879,"description":1880,"order":1824,"createdAt":1881,"updatedAt":1881},"demo-v2-topic-matematika-smp-1","teorema-pythagoras","Teorema Pythagoras","Teorema Pythagoras a² + b² = c² untuk mencari sisi miring dan sisi siku-siku, tripel Pythagoras, diagonal ruang balok, dan contoh soal kelas 8.","2026-10-08T23:58:22.690Z",{"id":1883,"subjectId":207,"levelId":136,"parentId":17,"slug":1884,"name":1885,"description":1886,"order":1824,"createdAt":1887,"updatedAt":1887},"demo-v2-topic-pemrograman-smp-1","variabel-dan-tipe-data-python","Variabel dan Tipe Data Python","Belajar variabel dan tipe data Python dari nol: int, float, string, boolean, operator, print, dan input, lengkap dengan contoh program dan latihan.","2026-10-08T23:58:23.562Z",{"id":1889,"subjectId":207,"levelId":100,"parentId":17,"slug":1890,"name":1891,"description":1892,"order":1893,"createdAt":1894,"updatedAt":1894},"demo-v2-topic-pemrograman-kuliah-2","class-dan-object-python","Class dan Object Python","Pelajari class dan object Python untuk OOP: __init__, self, atribut, method, inheritance, dan invarian objek lewat contoh program dompet digital.",101,"2026-10-08T23:58:23.830Z",{"id":1896,"subjectId":196,"levelId":140,"parentId":17,"slug":1897,"name":1898,"description":1899,"order":1893,"createdAt":1900,"updatedAt":1900},"demo-v2-topic-matematika-sma-2","eksponen-dan-logaritma","Eksponen dan Logaritma","Materi eksponen dan logaritma kelas 10: sifat-sifat eksponen, definisi dan sifat logaritma, persamaan eksponen dan logaritma, serta contoh soal.","2026-10-08T23:58:22.902Z",{"id":1902,"subjectId":20,"levelId":132,"parentId":17,"slug":1903,"name":1904,"description":1905,"order":1893,"createdAt":1906,"updatedAt":1906},"demo-v2-topic-fisika-sd-2","macam-macam-gaya","Gaya dan Macam-Macamnya","Gaya adalah tarikan atau dorongan. Pelajari macam-macam gaya (otot, gravitasi, magnet, gesek, pegas), pengaruhnya pada benda, dan contoh soalnya.","2026-10-08T23:58:23.126Z",{"id":1908,"subjectId":196,"levelId":132,"parentId":17,"slug":1909,"name":1910,"description":1911,"order":1893,"createdAt":1912,"updatedAt":1912},"demo-v2-topic-matematika-sd-2","rumus-keliling-dan-luas-bangun-datar","Keliling dan Luas Bangun Datar","Rumus keliling dan luas bangun datar: persegi, persegi panjang, segitiga, jajargenjang, trapesium, dan lingkaran, dengan cara mudah dan contoh soal.","2026-10-08T23:58:22.588Z",{"id":1914,"subjectId":207,"levelId":140,"parentId":17,"slug":1915,"name":1916,"description":1917,"order":1893,"createdAt":1918,"updatedAt":1918},"demo-v2-topic-pemrograman-sma-2","list-dan-dictionary-python","List dan Dictionary Python","Pahami list dan dictionary Python: indeks, append, key-value, get, dan perulangan, plus perbedaan keduanya lewat contoh pengolahan data nilai siswa.","2026-10-08T23:58:23.694Z",{"id":1920,"subjectId":20,"levelId":136,"parentId":17,"slug":1921,"name":1922,"description":1923,"order":1893,"createdAt":1924,"updatedAt":1924},"demo-v2-topic-fisika-smp-2","rumus-massa-jenis","Massa Jenis","Rumus massa jenis ρ = m\u002FV lengkap dengan satuan kg\u002Fm³ dan g\u002Fcm³, tabel massa jenis air, besi, dan minyak, cara menghitung, serta contoh soal pembahasan.","2026-10-08T23:58:23.217Z",{"id":1926,"subjectId":207,"levelId":136,"parentId":17,"slug":1927,"name":1928,"description":1929,"order":1893,"createdAt":1930,"updatedAt":1930},"demo-v2-topic-pemrograman-smp-2","percabangan-python-if-else","Percabangan Python","Pelajari percabangan Python dengan if, elif, dan else: operator perbandingan, operator logika, dan contoh program nilai rapor lengkap dengan outputnya.","2026-10-08T23:58:23.592Z",{"id":1932,"subjectId":207,"levelId":132,"parentId":17,"slug":1933,"name":1934,"description":1935,"order":1893,"createdAt":1936,"updatedAt":1936},"demo-v2-topic-pemrograman-sd-2","percabangan-dalam-algoritma","Percabangan dalam Algoritma","Percabangan dalam algoritma memilih tindakan berdasarkan syarat jika-maka. Pelajari pengertian, contoh sehari-hari, dan simbol flowchart-nya.","2026-10-08T23:58:23.503Z",{"id":1938,"subjectId":196,"levelId":136,"parentId":17,"slug":1939,"name":1940,"description":1941,"order":1893,"createdAt":1942,"updatedAt":1942},"demo-v2-topic-matematika-smp-2","persamaan-garis-lurus","Persamaan Garis Lurus","Persamaan garis lurus y = mx + c, rumus gradien dari dua titik, garis sejajar dan tegak lurus, cara menggambar grafik, serta contoh soal kelas 8.","2026-10-08T23:58:22.730Z",{"id":160,"subjectId":20,"levelId":100,"parentId":17,"slug":148,"name":161,"description":150,"order":1893,"createdAt":1944,"updatedAt":1944},"2026-10-08T23:58:23.394Z",{"id":1946,"subjectId":196,"levelId":140,"parentId":17,"slug":1947,"name":1948,"description":1949,"order":1950,"createdAt":1951,"updatedAt":1951},"demo-v2-topic-matematika-sma-3","rumus-peluang","Peluang Kejadian","Rumus peluang P(A) = n(A)\u002Fn(S), ruang sampel, peluang komplemen, frekuensi harapan, kejadian saling lepas dan saling bebas, plus contoh soal dadu dan koin.",102,"2026-10-08T23:58:22.934Z",{"id":1953,"subjectId":207,"levelId":140,"parentId":17,"slug":1954,"name":1955,"description":1956,"order":1950,"createdAt":1957,"updatedAt":1957},"demo-v2-topic-pemrograman-sma-3","pencarian-linear-dan-biner","Pencarian Linear dan Biner","Pelajari pencarian linear dan pencarian biner (binary search): cara kerja, syarat data terurut, kode Python, dan perbandingan jumlah langkahnya.","2026-10-08T23:58:23.724Z",{"id":1959,"subjectId":207,"levelId":136,"parentId":17,"slug":1960,"name":1961,"description":1962,"order":1950,"createdAt":1963,"updatedAt":1963},"demo-v2-topic-pemrograman-smp-3","perulangan-python-for-while","Perulangan Python","Pelajari perulangan Python dengan for, range(), dan while, lengkap dengan contoh program menghitung total, break, continue, dan latihan soal.","2026-10-08T23:58:23.624Z",{"id":1965,"subjectId":207,"levelId":132,"parentId":17,"slug":1966,"name":1967,"description":1968,"order":1950,"createdAt":1969,"updatedAt":1969},"demo-v2-topic-pemrograman-sd-3","perulangan-dalam-algoritma","Perulangan dalam Algoritma","Perulangan dalam algoritma mengulang langkah yang sama beberapa kali. Pelajari pengertian, contoh perulangan sehari-hari, dan cara menghitung hasilnya.","2026-10-08T23:58:23.529Z",{"id":1971,"subjectId":196,"levelId":136,"parentId":17,"slug":1972,"name":1973,"description":1974,"order":1950,"createdAt":1975,"updatedAt":1975},"demo-v2-topic-matematika-smp-3","rumus-prisma-dan-limas","Prisma dan Limas","Rumus volume prisma dan limas, luas permukaan, sifat sisi-rusuk-titik sudut, jaring-jaring, limas 3D interaktif, dan contoh soal bangun ruang sisi datar.","2026-10-08T23:58:22.780Z",{"id":1977,"subjectId":207,"levelId":100,"parentId":17,"slug":1978,"name":1979,"description":1980,"order":1950,"createdAt":1981,"updatedAt":1981},"demo-v2-topic-pemrograman-kuliah-3","unit-test-python","Unit Test Python","Pelajari unit test Python dengan modul unittest: assertEqual, assertRaises, nilai batas, dan cara menjalankan tes, lengkap dengan contoh dan versi pytest.","2026-10-08T23:58:23.864Z",{"id":1983,"subjectId":196,"levelId":100,"parentId":17,"slug":1984,"name":1985,"description":1986,"order":1950,"createdAt":1987,"updatedAt":1987},"demo-v2-topic-matematika-kuliah-3","vektor-3-dimensi-dot-product","Vektor 3D dan Dot Product","Vektor 3 dimensi: komponen, panjang vektor, vektor satuan, dot product atau perkalian titik, sudut antara dua vektor, proyeksi, dan contoh soal.","2026-10-08T23:58:23.045Z",{"id":1989,"subjectId":196,"levelId":132,"parentId":17,"slug":1990,"name":1991,"description":1992,"order":1950,"createdAt":1993,"updatedAt":1993},"demo-v2-topic-matematika-sd-3","rumus-volume-kubus","Volume dan Luas Permukaan Kubus","Rumus volume kubus V = s³ dan luas permukaan kubus L = 6s², sifat kubus, jaring-jaring, kubus 3D interaktif, dan contoh soal bertingkat.","2026-10-08T23:58:22.619Z",{"id":1995,"subjectId":196,"levelId":136,"parentId":17,"slug":1996,"name":1997,"description":1998,"order":1999,"createdAt":2000,"updatedAt":2000},"demo-v2-topic-matematika-smp-4","rumus-tabung-dan-kerucut","Tabung dan Kerucut","Rumus volume tabung dan kerucut, luas permukaan, garis pelukis, jaring-jaring berupa persegi panjang dan juring, kerucut 3D interaktif, dan contoh soal.",103,"2026-10-08T23:58:22.828Z",{"id":2002,"subjectId":207,"levelId":140,"parentId":17,"slug":2003,"name":2004,"description":2005,"order":1999,"createdAt":2006,"updatedAt":2006},"demo-v2-topic-pemrograman-sma-4","try-except-python","Try Except dan Membaca File","Pelajari try except Python untuk menangani error seperti ValueError dan FileNotFoundError, serta cara membaca dan menulis file txt dengan with open.","2026-10-08T23:58:23.755Z",{"id":2008,"subjectId":196,"levelId":132,"parentId":17,"slug":2009,"name":2010,"description":2011,"order":1999,"createdAt":2012,"updatedAt":2012},"demo-v2-topic-matematika-sd-4","rumus-volume-balok","Volume dan Luas Permukaan Balok","Rumus volume balok V = p × l × t dan luas permukaan balok L = 2(pl + pt + lt), sifat balok, jaring-jaring, balok 3D interaktif, dan contoh soal.","2026-10-08T23:58:22.651Z",[]]