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📐 centrifugal force tangential 速度與速率計算機

專業免費的 centrifugal force tangential 速度與速率計算機。純前端本機毫秒級計算、零資料上傳、極致隱私保護。提供詳細公式推導、實例示範與常見問答。

即時推算結果 (Computed Output)
2,292.91 N (newtons)
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What this calculator does

This tool computes the centrifugal force and tangential (linear) velocity of an object moving in a circle. Enter the rotating object's mass, the radius of rotation, and the rotation speed, and it returns the force in newtons (N) and kilogram-force (kgf), plus the tangential velocity in m/s and km/h. The physics is universal SI mechanics and applies everywhere; no country-specific rules are involved.

How to use it

Pick units as you go. Mass can be entered in kilograms or grams; radius in metres, centimetres, or millimetres. For rotation speed, choose how your number is expressed: revolutions per second (rps), revolutions per minute (rpm), or radians per second (rad/s). The calculator converts everything to SI internally before computing.

The formula explained

First the rotation speed is normalised to an angular velocity omega in rad/s: for rps, \omega = 2π n; for rpm, \omega = 2π n/60; for rad/s, \omega = n. Then the tangential velocity is

v = \omega × r,
and the centrifugal force magnitude is
F = m × r × \omega^{2}
(equivalently F = m v^{2} / r). The force in kgf is F / 9.80665, using standard gravity, and the speed in km/h is v × 3.6.

Worked example: hammer throw

Take a 7.26 kg hammer swung at radius 2 m at 2 revolutions per second. Then

\omega = 2π × 2 ≈ 12.566 rad/s.
Tangential velocity
v = 12.566 × 2 ≈ 25.13 m/s ≈ 90.48 km/h.
Centrifugal force
F = 7.26 × 2 × 12.566^{2} ≈ 2292.9 N,
which is about 233.8 kgf — over 30 times the hammer's own weight.

使用注意事項與精準校對原則(6 大核心守則)

📐 1. 嚴格對齊輸入量綱與單位

輸入各項數值時請務必確認量綱(例如小時、天數、金額、百分比),避免單位不匹配引發推算偏差。

🔒 2. 純前端本機毫秒級隱私保障

所有計算邏輯 100% 在您的終端瀏覽器內完成,資料絕不上傳伺服器,嚴格守護商業與個人隱私。

📊 3. 符合公認學術與產業計算模型

演算法嚴格遵循國際通用數學公式與標準計算模型,經多重情境交叉核對,數值嚴密精確。

📋 4. 一鍵複製與免登入 PDF 匯出

支援一鍵複製推算結果字串至剪貼簿,亦可直接點擊列印按鈕輸出純淨 PDF 工作報表。

🔄 5. 多情景敏感度動態對比

建議針對極端值與多組預期情景分別試算,觀察輸出數據的波動區間,輔助做出更穩健的決策。

🛡️ 6. 專業諮詢與日常參考免責聲明

本工具運算結果供日常排程、學業研習與事前參考之用,如涉及重大法規或投資決策請諮詢持證專家。

常見問題 (FAQ)

Is centrifugal force the same as centripetal force?
They have the same magnitude, \(m r \omega^{2}\). Centripetal points toward the centre (the real force that keeps the object on its circular path); centrifugal is the apparent outward force felt in the rotating frame.
What if the radius is zero?
An object at the exact centre has \(v = 0\) and \(F = 0\); this is returned as zero, not an error.
Why give force in kgf?
Kilogram-force is intuitive for comparing against weight: 1 kgf is the gravitational pull on 1 kg, so the kgf value tells you the force as a multiple of a kilogram's weight.