Flywheel spin-down time
A 2 kg·m² flywheel spinning at 10 rad/s under a constant 4 N·m brake stops in 5 s, losing 2 rad/s every second. Enter inertia, initial speed and brake torque to get the stopping time for brake sizing or safety notes. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Moment of inertia
- 2
- Initial angular speed
- 10
- Braking torque
- 4
- Angular deceleration
- 2
- Spin down time s
- 5
A spinning flywheel, rotor, or machine shaft does not stop instantly when you apply a brake. Under a constant braking torque the angular speed falls linearly, and the time to reach rest is the ratio of angular momentum I·ω to that torque. Use it for flywheel sizing checks, brake sizing notes, homework on rotational dynamics, and any pipeline that needs a repeatable coast-to-stop figure without spreadsheets or one-off scripts. Zero braking torque is rejected because division by zero is undefined and implies infinite spin-down time.
What spin-down time means under constant torque
Newton’s second law for rotation says torque equals moment of inertia times angular acceleration: τ = I·α. When the braking torque is constant in magnitude and opposes rotation, the angular deceleration is the constant α = τ/I. Starting from an initial angular speed ω₀ and decelerating at constant α, the body reaches zero speed in time t = ω₀/α, which rearranges to the compact form t = I·ω₀/τ.
That is the coast-down or spin-down interval under an ideal constant-torque brake. Real machines add viscous drag, stick-slip at low speed, and thermal limits on the brake, but the rigid-body constant-torque model remains the baseline every design note, lab report, and control sketch starts from. Moment of inertia must be positive; a zero or negative I is not a physical rigid body for this formula.
Initial angular speed must be non-negative in rad/s; zero speed simply returns zero time. Units are SI throughout—kg·m², rad/s, N·m, and seconds—so convert rpm to rad/s (multiply by 2π/60) and any non-SI inertia before calling if your datasheet uses other conventions.
What you can do with it
Flywheel and rotor brake sizing
Estimate stop time from inertia, initial speed, and constant brake torque before locking pad or clutch selections.
Safety coast-down documentation
Document how long a high-inertia shaft takes to stop under a specified torque for test protocols and machine safety notes.
FAQ
How is spin-down time calculated?
The response also returns angular deceleration α = τ/I in rad/s².
What units should I use?
Time is returned in seconds. Convert rpm with rad/s = rpm × 2π/60 before calling.
What if braking torque is zero?
Zero torque implies infinite spin-down time, so division by zero is rejected before any result is returned; failed tasks are not charged.
Does this model friction that varies with speed?
No. It assumes constant braking torque magnitude. For viscous drag, stick-slip, or multi-stage brakes you must integrate a different torque law offline, then use this only for the constant-torque segment.
Should I enter the braking torque as a negative number?
No. Enter the positive size of the brake torque, even though it opposes the rotation. A negative torque is refused, and so is zero, because a brake with no torque would never stop the rotor.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/mech/spin-down-time \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"moment_of_inertia":2,"initial_angular_speed":10,"braking_torque":4}'const res = await fetch("https://api.kit.forhosting.com/mech/spin-down-time", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"moment_of_inertia": 2,
"initial_angular_speed": 10,
"braking_torque": 4
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/mech/spin-down-time",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"moment_of_inertia": 2,
"initial_angular_speed": 10,
"braking_torque": 4
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/mech/spin-down-time", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"moment_of_inertia":2,"initial_angular_speed":10,"braking_torque":4}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"moment_of_inertia":2,"initial_angular_speed":10,"braking_torque":4}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/mech/spin-down-time", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"moment_of_inertia": 2,
"initial_angular_speed": 10,
"braking_torque": 4
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "mech.spin_down_time",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
This capability performs that classical rigid-body calculation deterministically: three finite numbers in, spin-down time in seconds plus angular deceleration out, with a fixed twelve-decimal rounding policy so browser and API results match byte for byte.
What spin-down time means under constant torque
Braking torque must be strictly positive: zero torque never stops the rotor, and the API rejects it with invalid_input so you never receive a silent infinity or NaN.
Inputs, outputs, and validation rules
All three must be finite. Moment of inertia and braking torque must be strictly greater than zero; initial angular speed must be greater than or equal to zero. Negative torque is also rejected: pass the positive magnitude of the braking torque rather than a signed opposing value. Convert rpm, degrees per second, or g·cm² offline if your source data are not already in SI angular units. Send three required numbers: moment_of_inertia for I in kilogram square meters, initial_angular_speed for ω₀ in radians per second, and braking_torque for the constant brake magnitude τ in newton-meters. A braking_torque of exactly zero fails with invalid_input and a message that names the field, because t = I·ω/τ would divide by zero and failed tasks are not charged. A classic check is I = 2 kg·m², ω₀ = 10 rad/s, and τ = 4 N·m, which yields angular deceleration 2 rad/s² and spin-down time 5 s.
Where teams plug spin-down time into workflows
Mechanical engineers estimate how long a flywheel or high-inertia shaft takes to stop under a specified brake torque before they size pads, clutch packs, or regenerative limits. Test technicians document coast-down targets for acceptance tests when a rig must stop within a safety window. Documentation writers include live examples so readers can change I, ω, and τ without leaving the page. Product teams embed the free browser form on study pages and call the API from design calculators or batch scripts that sweep inertia and torque grids. Because each successful call is a single analytic item priced at $0.002, automation can evaluate many design points without model cost or subscription overhead. Prefer this endpoint when you already know moment of inertia, initial angular speed, and a constant braking torque magnitude—and only need the transparent stop time—not a full multi-stage brake model, friction map, or energy-dissipation thermal simulation, which need richer inputs and different tooling.
Integration use cases
Rotational dynamics homework checks
Compute expected spin-down times for rigid-body problems so instructors and students share a deterministic golden answer.
Technical questions
How much does each API call cost?
$0.002 per successful request. The browser tool above runs free locally; the API draws from your prepaid KIT balance only when the task succeeds.