Inersia Rotasi
| English | Bahasa Indonesia |
|---|---|
| rotational inertia/rəʊˈteɪʃənl ɪˈnɜːʃə/ | inersia rotasi |
A skater spins faster by pulling her arms in
- A figure skater spins slowly with arms outstretched, then pulls them in and whirls into a blur.
- She added no push — she just moved her mass closer to the axis.
- How hard something is to spin depends on where its mass sits, not only how much.
- This "rotational stubbornness" is called rotational inertia 转动惯量.
Mass distribution is everything
- Rotational inertia (moment of inertia) $I$ measures resistance to angular acceleration.
- For point masses: $I = \sum m r^2$ — each bit of mass counts by its distance squared.
- Mass far from the axis contributes far more than mass near it.
- Units are $\text{kg}\cdot\text{m}^2$.
Dua bola $0.5\ \text{kg}$ berada $2\ \text{m}$ dari sumbu pada batang ringan. Berapakah inersia rotasinya, dalam $\text{kg}\cdot\text{m}^2$?
$I = \sum mr^2 = 2 \times (0.5 \times 2^2) = 4\ \text{kg}\cdot\text{m}^2$.
Inersia rotasi bergantung pada:
$I = \sum mr^2$ bergantung pada baik massa maupun jaraknya dari sumbu (dikuadratkan).
Untuk massa titik, inersia rotasi adalah jumlah dari $m r^{\_\_}$. Isi pangkatnya.
$I = \sum m r^2$ — jarak muncul dikuadratkan.
Gerakkan dua bola $0.5\ \text{kg}$ yang sama ke $1\ \text{m}$ dari sumbu. Berapakah inersia rotasi barunya, dalam $\text{kg}\cdot\text{m}^2$?
$I = 2 \times (0.5 \times 1^2) = 1\ \text{kg}\cdot\text{m}^2$ — setengah $r$ menjadi seperempat $I$.
Shape matters, so it has standard formulas
- The same mass can have very different $I$ depending on its shape and axis.
- A hollow ring (all mass at the rim) has more $I$ than a solid disk of the same mass.
- Standard shapes have known formulas, e.g. a solid disk is $I = \tfrac12 M R^2$.
- The $r^2$ weighting is why hollow objects feel "heavier" to spin.
Dua benda memiliki massa yang sama. Pilih semua cara untuk membuat satu lebih sulit diputar daripada yang lain.
Memindahkan massa ke luar (tepi, cincin hollow) meningkatkan $I$. Warna tidak berpengaruh.
Back to the skater
- Pulling her arms in shrinks $r$, so her $I$ drops sharply (because of the $r^2$).
- With angular momentum conserved (next topic), a smaller $I$ means a larger $\omega$ — she speeds up.
- Divers and gymnasts tuck for the same reason: small $I$, fast spin.
- Extend again and the spin slows back down.
Inersia rotasi lebih besar atau lebih kecil?
Inersia rotasi bergantung pada seberapa jauh massa berada dari sumbu. Urutkan setiap kasus.
Pengguna es yang berputar mempercepat saat menarik lengannya karena inersia rotasinya berkurang.
Inersia $r$ yang lebih kecil berarti momentum sudut $I$ yang lebih kecil; dengan kekekalan momentum sudut, $\omega$ meningkat.
Rotational inertia is not just mass — it depends on how the mass is arranged. Two objects of equal mass can be very different to spin. Because of the $r^2$, mass at the rim matters far more than mass near the axis.
Two $0.5\ \text{kg}$ balls sit on a light rod, each $2\ \text{m}$ from the axis.
- $I = \sum m r^2 = 2 \times (0.5 \times 2^2) = 2 \times 2 = 4\ \text{kg}\cdot\text{m}^2$.
Move them to $1\ \text{m}$ and $I$ drops to $2 \times (0.5 \times 1) = 1\ \text{kg}\cdot\text{m}^2$ — four times smaller.
Rotational inertia $I$ is the resistance to angular acceleration: $I = \sum mr^2$. It depends on where the mass sits (distance squared), not just how much — so a skater pulling her arms in lowers $I$ and spins faster. Units: $\text{kg}\cdot\text{m}^2$.