Angular Acceleration Definition
The rotational movement of an object is usually described by a physical quantity called angular velocity. It measures the angle by which an object rotates in a specific time. For example, imagine that a carousel in an amusement park performs a full rotation within ten seconds. Its angular velocity is one rotation (360°) per ten seconds, or 36° per second.
Let's assume that our carousel starts to rotate faster and faster — not 36° but 50°, then 64° per second. Angular acceleration describes this rate of change of angular velocity and is caused by torque.
Angular Acceleration Formula
Angular acceleration can be computed in two different ways:
- Method 1 — from angular velocity change:
α = (ω₂ − ω₁) / t - Method 2 — from tangential acceleration:
α = a / R
Where:
- α — Angular acceleration (rad/s²)
- ω₁ — Initial angular velocity
- ω₂ — Final angular velocity
- t — Time of change of angular velocity
- a — Tangential acceleration (linear acceleration perpendicular to the radius)
- R — Radius of the circle (distance from the axis of rotation)
Angular Acceleration Units
This calculator provides results in four common units of angular acceleration:
- rad/s² — Radians per second squared (SI base unit)
- °/s² — Degrees per second squared
- rpm/s — Revolutions per minute per second (common in engineering)
- rpm² — Revolutions per minute squared
Unit conversions:
- 1 rad/s² = 57.2958 °/s²
- 1 rad/s² = 9.5493 rpm/s
- 1 rad/s² = 91.189 rpm²
Supported Unit Systems
The calculator supports both major unit systems:
- Metric: angular velocity in rad/s or °/s; tangential acceleration in m/s²; radius in m or cm
- American (Imperial): angular velocity in rpm; tangential acceleration in ft/s²; radius in ft or in
FAQs
What is the difference between angular velocity and angular acceleration?
Angular velocity (ω) measures how fast an object rotates (angle per unit time). Angular acceleration (α) measures how quickly the angular velocity changes (angular velocity per unit time). If a wheel spins at a constant speed, its angular acceleration is zero even if the angular velocity is large.
What causes angular acceleration?
Angular acceleration is caused by a net torque acting on a rotating object. According to Newton's second law for rotation: τ = I × α, where τ is torque and I is the moment of inertia.
Can angular acceleration be negative?
Yes. Negative angular acceleration means the object is slowing down in the positive direction of rotation (deceleration). For example, if ω₁ = 10 rad/s and ω₂ = 4 rad/s over 3 seconds, the angular acceleration is (4 − 10) / 3 = −2 rad/s².
What is tangential acceleration?
Tangential acceleration acts as a linear acceleration which is perpendicular to the radius of the circle. It is directly related to angular acceleration by: a = α × R. This is how Method 2 (α = a / R) is derived.
How do I convert rad/s² to rpm/s?
Multiply the value in rad/s² by 60 / (2π) ≈ 9.5493. For example, 2 rad/s² × 9.5493 ≈ 19.10 rpm/s.