🔄 转动动能Rotational Kinetic Energy Calculator

使用说明与常见问题How-to & FAQ

「转动动能」是什么？What is the Rotational Kinetic Energy Calculator tool?

E = ½ I ω²：I 为转动惯量，ω 为角速度（可用 rpm 换算）；常见物体的 I 也可由质量和尺寸估算。本地处理。E = ½ I ω² for moment of inertia I and angular speed ω (rpm supported); I can also be estimated from mass and size for common shapes. Processed locally.

如何使用「转动动能」？How do I use the Rotational Kinetic Energy Calculator tool?

填写转动惯量和转速（rpm），即可得到转动动能 E = ½Iω²；不知道转动惯量时可留空，并选择形状、填写质量和半径来估算。结果会随输入实时更新。Enter the moment of inertia and the speed in rpm to get the rotational kinetic energy E = ½Iω²; if you don't know the moment of inertia, leave it blank and choose a shape and enter the mass and radius to estimate it. The result updates as you type.

滚动？Rolling?

纯滚动总动能 = ½ mv² + ½ I ω²，且 v = ω r。For pure rolling total KE = ½ mv² + ½ I ω² with v = ω r.

能举个计算实例吗？Can you show a worked example?

例如在「转动动能」中填 转动惯量 kg·m²（或留空估算） = 2，转速 rpm = 300，估算形状 = 实心圆盘（轴过中心），质量 kg（估算用） = 1，半径 / 半长 m（估算用） = 0.2，结果区显示：转动惯量 I：2 kg·m²；角速度 ω：31.4159 rad/s；转动动能：986.9604 JFor example, entering Moment of inertia kg·m² (or blank to estimate) = 2, Speed rpm = 300, Shape for estimate = Solid disk, Mass kg (for estimate) = 1, Radius / half-length m (for estimate) = 0.2 in the Rotational Kinetic Energy Calculator gives: Moment of inertia I: 2 kg·m²; Angular velocity ω: 31.4159 rad/s; Rotational KE: 986.9604 J

哪些输入会被检查？Which inputs are validated?

「转动动能」会检查这些输入——「转动惯量 kg·m²（或留空估算）」：不能为负数；「转速 rpm」：必须填写；「质量 kg（估算用）」、「半径 / 半长 m（估算用）」：必须填写，须大于 0；绝对值超过 10¹⁵ 的数也会被拒绝。不符合时结果区显示具体提示，不会给出数字。The Rotational Kinetic Energy Calculator checks its inputs — "Moment of inertia kg·m² (or blank to estimate)": cannot be negative; "Speed rpm": required; "Mass kg (for estimate)", "Radius / half-length m (for estimate)": required, must be greater than 0; numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the problem instead of showing a number.

有哪些选项可以调整？What options can I adjust?

「转动动能」的设置：「转动惯量 kg·m²（或留空估算）」默认 2；「转速 rpm」默认 300；「估算形状」可选 实心圆盘（轴过中心）、实心球、细圆环、细杆（绕一端）（默认 实心圆盘（轴过中心））；「质量 kg（估算用）」默认 1；「半径 / 半长 m（估算用）」默认 0.2。每次生成结果都按当前设置处理。Settings in the Rotational Kinetic Energy Calculator — "Moment of inertia kg·m² (or blank to estimate)" default 2; "Speed rpm" default 300; "Shape for estimate": Solid disk, Solid sphere, Thin hoop, Thin rod end (default Solid disk); "Mass kg (for estimate)" default 1; "Radius / half-length m (for estimate)" default 0.2. The result always uses the current settings.

计算结果可以用于作业或工程吗？Can I use the results for homework or engineering?

「转动动能」使用教科书标准公式（公式写在说明和常见问题中），适合学习和估算核对；涉及安全的工程设计请以规范和实测为准。The Rotational Kinetic Energy Calculator uses standard textbook formulas (given in the description and FAQ), which is good for learning and checking estimates; for safety-critical engineering follow codes and measured values.

「转动动能」免费吗？需要注册吗？Is the Rotational Kinetic Energy Calculator free? Do I need an account?

「转动动能」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Rotational Kinetic Energy Calculator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.