# Angular Velocity Calculator

Convert angular velocity between rad/s, RPM, and deg/s. Calculate linear velocity and period from angular velocity and radius.

## What this calculates

Angular velocity measures how fast an object rotates or revolves. This calculator converts between the three common units (radians per second, RPM, and degrees per second) and optionally calculates the linear (tangential) velocity at a given radius. It also provides the period of rotation.

## Inputs

- **Input Unit** — options: rad/s, RPM, deg/s — Select the unit of the angular velocity input.
- **Angular Velocity** — Angular velocity value in the selected unit.
- **Radius (optional)** (m) — min 0 — Radius of rotation. If provided, linear velocity will be calculated.

## Outputs

- **Angular Velocity** (rad/s) — Radians per second
- **Angular Velocity** (RPM) — Revolutions per minute
- **Angular Velocity** (°/s) — Degrees per second
- **Linear (Tangential) Velocity** (m/s) — v = ωr (requires radius input)
- **Period** (s) — Time for one full revolution: T = 2π/ω

## Details

Angular velocity (ω) describes rotational speed. The SI unit is radians per second (rad/s), where one full revolution equals 2π radians. RPM (revolutions per minute) is common in engineering and everyday use, while degrees per second is intuitive for angles.

The conversion formulas: ω (rad/s) = RPM × 2π/60 = deg/s × π/180. When combined with a radius, angular velocity gives the linear (tangential) velocity: v = ωr. A point on the rim of a wheel spinning at 100 RPM with radius 0.3 m moves at v = (100 × 2π/60) × 0.3 ≈ 3.14 m/s.

Angular velocity is fundamental to rotational mechanics, motor specifications, centrifuge calculations, wheel dynamics, and satellite orbits. The period T = 2π/ω gives the time for one complete revolution, useful for determining orbital periods or the cycle time of rotating machinery.

## Frequently Asked Questions

**Q: What is the difference between angular velocity and linear velocity?**

A: Angular velocity (ω) measures how fast an object rotates (in rad/s or RPM). Linear velocity (v) measures how fast a point moves along its circular path (in m/s). They are related by v = ωr, where r is the distance from the axis of rotation.

**Q: How do I convert RPM to rad/s?**

A: Multiply RPM by 2π/60. For example, 3000 RPM = 3000 × 2π/60 = 314.16 rad/s. This works because each revolution is 2π radians and there are 60 seconds in a minute.

**Q: What is a radian?**

A: A radian is the angle subtended at the center of a circle by an arc equal in length to the radius. One full revolution is 2π radians (≈ 6.283 rad), equivalent to 360°. Radians are dimensionless and are the natural unit for angular measurement in physics.

**Q: Why does a point farther from the center move faster?**

A: All points on a rigid rotating body have the same angular velocity ω, but linear velocity v = ωr increases with radius r. A point on the rim of a wheel travels a larger circular path in the same time as a point near the center, so it must move faster.

**Q: What is the period of rotation?**

A: The period T is the time for one complete revolution: T = 2π/ω (in seconds). It is the inverse of frequency: T = 1/f. Earth's rotational period is about 86,164 seconds (23 hours 56 minutes for a sidereal day).

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Source: https://vastcalc.com/calculators/physics/angular-velocity
Category: Physics
Last updated: 2026-04-21