---
title: "Angular Acceleration (α) — AP Physics 1 Definition & Guide"
description: "Angular acceleration (α) is the rate of change of angular velocity, in rad/s². It's the rotational version of a, linked to torque by τ_net = Iα in AP Physics 1."
canonical: "https://fiveable.me/ap-physics-1-revised/key-terms/angular-acceleration-a"
type: "key-term"
subject: "AP Physics 1"
unit: "Unit 3"
---

# Angular Acceleration (α) — AP Physics 1 Definition & Guide

## Definition

Angular acceleration (α) is the rate at which an object's angular velocity (ω) changes over time, measured in radians per second squared (rad/s²). In AP Physics 1 it plays the same role for rotation that linear acceleration plays for straight-line motion, and it's produced by a net torque (α = τ_net / I).

## What It Is

[Angular acceleration](/ap-physics-1-revised/key-terms/angular-acceleration "fv-autolink") (α) tells you how fast an object's spin rate is changing. If a wheel speeds up from 2 rad/s to 6 rad/s, it has a positive angular acceleration; if it slows down, α points opposite to ω. Mathematically, α = Δω/Δt, and its units are rad/s².

Here's the move that makes rotation feel easy: angular acceleration is just linear [acceleration](/ap-physics-1-revised/unit-1/5-vectors-and-motion-in-two-dimensions/study-guide/LvdiAzU3amzMqu6O "fv-autolink") with the variables swapped. Every [kinematics](/ap-physics-1-revised/unit-1 "fv-autolink") equation you learned in Unit 1 has a rotational twin. Replace x with θ, v with ω, and a with α, and the equations work exactly the same way (ω = ω₀ + αt, θ = ω₀t + ½αt², and so on). The cause-and-effect story also mirrors translation. A net force causes linear acceleration through F_net = ma, and a net torque causes angular acceleration through τ_net = Iα, where moment of inertia I is the rotational version of mass. For a point on the rotating object a distance r from the axis, angular and linear quantities connect through a_tangential = rα.

## Why It Matters

Angular acceleration lives at the heart of [Unit 5](/ap-physics-1-revised/unit-5 "fv-autolink") (Torque and Rotational Dynamics) in the revised [AP Physics 1](/ap-physics-1-revised "fv-autolink") course. Rotational kinematics, the very first topic of that unit, is built around describing motion with θ, ω, and α, and the unit's big payoff equation, τ_net = Iα, is Newton's second law rewritten for rotation. If you can't read α off a graph or solve for it from a net torque, most of Unit 5 is locked.

It also matters because the exam loves analogy questions. The CED frames rotation as a parallel structure to translation, so questions constantly test whether you can translate between the two worlds. Knowing that α is to ω what a is to v, and that [torque](/ap-physics-1-revised/unit-5/3-torque/study-guide/I9b5y8FshkMfALc5 "fv-autolink") is to α what force is to a, lets you reuse everything from Units 1-2 instead of memorizing a new physics from scratch.

## Connections

### [Angular Velocity (ω) (Unit 5)](/ap-physics-1-revised/key-terms/angular-velocity-w)

Angular acceleration is the rate of change of [angular velocity](/ap-physics-1-revised/key-terms/angular-velocity "fv-autolink"), exactly like a is the rate of change of v. On an ω-versus-t graph, α is the slope. An object can have a big ω with zero α (steady spin) or zero ω with a big α (just starting to rotate).

### Torque (Unit 5)

[Net torque](/ap-physics-1-revised/key-terms/net-torque "fv-autolink") is what causes angular acceleration, through τ_net = Iα. This is the rotational Newton's second law, so every 'find the angular acceleration' problem usually starts with 'find the net torque.'

### [Moment of Inertia (Unit 5)](/ap-physics-1-revised/key-terms/moment-of-inertia)

Moment of inertia plays the role of mass in τ_net = Iα. The same torque produces a smaller α on an object with mass spread far from the axis, which is why a figure skater pulling in her arms spins up so fast.

### [Uniform Circular Motion (Unit 2)](/ap-physics-1-revised/key-terms/uniform-circular-motion)

Uniform circular motion is the special case where α = 0. The speed around the circle is constant, so ω never changes, even though there's still a centripetal acceleration pointing toward the center. Recognizing 'constant speed in a circle means zero angular acceleration' kills a lot of trap answer choices.

## On the AP Exam

Expect angular acceleration in multiple-choice stems that give you an ω-versus-t graph and ask for α (it's the slope), or that describe a torque applied to a disk or rod and ask you to rank or calculate α using τ_net = Iα. Rotational kinematics questions hand you two of θ, ω, α, and t and ask for the third, using the same equation structure as linear kinematics. On the free-response side, rotation shows up in derivations and experimental design, like measuring α of a pulley from the linear acceleration of a hanging mass using a = rα, or arguing why α changes when mass is redistributed (I changes, torque doesn't). The most common skill tested is justification, meaning you explain in words why α increases, decreases, or stays zero, not just plug numbers.

## Angular Acceleration (α) vs Centripetal acceleration

These are completely different quantities that both show up in circular motion. Centripetal acceleration (a_c = v²/r) points toward the center of the circle and changes the direction of velocity; it exists even when the spin rate is constant. Angular acceleration changes the spin rate itself. In uniform circular motion, a_c is nonzero but α = 0. A point on a speeding-up wheel has both at once: centripetal acceleration inward plus tangential acceleration (a_t = rα) along the direction of motion.

## Key Takeaways

- Angular acceleration (α) is the rate of change of angular velocity, α = Δω/Δt, measured in rad/s².
- Every linear kinematics equation has a rotational twin; swap x → θ, v → ω, and a → α and solve the same way.
- Net torque causes angular acceleration through τ_net = Iα, the rotational version of Newton's second law.
- Uniform circular motion has zero angular acceleration but nonzero centripetal acceleration, because the speed is constant while the direction keeps changing.
- A point at distance r from the rotation axis has tangential acceleration a_t = rα, which is how you connect a rotating pulley to a hanging mass in lab-style problems.
- On an ω-versus-t graph, angular acceleration is the slope, just like linear acceleration on a v-versus-t graph.

## FAQs

### What is angular acceleration in AP Physics 1?

Angular acceleration (α) is how quickly an object's angular velocity changes, defined as α = Δω/Δt and measured in rad/s². It's the rotational analog of linear acceleration and is caused by a net torque via τ_net = Iα.

### Is angular acceleration zero in uniform circular motion?

Yes. 'Uniform' means constant speed, so ω never changes and α = 0. The object still has centripetal acceleration toward the center because its direction is constantly changing, and that's a favorite trap on multiple choice.

### What's the difference between angular acceleration and angular velocity?

Angular velocity (ω) tells you how fast something is spinning right now, in rad/s. Angular acceleration (α) tells you how fast that spin rate is changing, in rad/s². A ceiling fan at constant speed has large ω but zero α.

### How do you find angular acceleration from torque?

Use the rotational form of Newton's second law, α = τ_net / I. Find the net torque on the object, divide by its moment of inertia, and you have α. Doubling the torque doubles α; doubling I cuts α in half.

### How is angular acceleration related to linear (tangential) acceleration?

For a point a distance r from the rotation axis, a_tangential = rα. This is the equation that links a spinning pulley to the string and hanging mass attached to it, which shows up constantly in AP Physics 1 lab and FRQ setups.

## Related Study Guides

- [Unit 3 Overview: Circular Motion and Gravitation](/ap-physics-1-revised/unit-3/review/study-guide/EYz8EQHLZdA71szqCh1G)

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