---
title: "Angular Acceleration — AP Physics C Mech Definition"
description: "Angular acceleration (α = dω/dt) is the rate of change of angular velocity, in rad/s². It links rotational kinematics to torque via τ = Iα on the AP exam."
canonical: "https://fiveable.me/ap-physics-c-mechanics/key-terms/angular-acceleration"
type: "key-term"
subject: "AP Physics C: Mechanics"
unit: "Unit 5"
---

# Angular Acceleration — AP Physics C Mech Definition

## Definition

Angular acceleration (α) is the rate of change of angular velocity with respect to time, α = dω/dt, measured in rad/s². It is the rotational analog of linear acceleration and connects directly to torque through Newton's second law for rotation, τ_net = Iα.

## What It Is

Angular acceleration, written α, tells you how fast an object's [angular velocity](/ap-physics-c-mechanics/key-terms/angular-velocity "fv-autolink") ω is changing. Mathematically, α = dω/dt = d²θ/dt², with units of radians per second squared (rad/s²). If a disk is spinning faster and faster, α points in the same direction as ω. If it's slowing down, α points opposite to ω. If α is constant, the rotational kinematics equations look exactly like the linear ones you learned in [Unit 1](/ap-physics-c-mechanics/unit-1 "fv-autolink"), just with θ swapped for x, ω for v, and α for a.

Here's the mental model that makes everything in [rotation](/ap-physics-c-mechanics/unit-5/1-rotation/study-guide/0tVqvv29lj9DIxVt "fv-autolink") click. Angular acceleration is to rotation what linear acceleration is to straight-line motion. Every translational idea has a rotational twin, and α is the twin of a. That analogy isn't just a memory trick. It's how the AP exam builds problems. A point at distance r from the axis has tangential acceleration a_t = rα, which is the bridge between the rotational world and the linear world. And just as F_net = ma governs linear motion, τ_net = Iα governs rotation. In Physics C, you should also be comfortable when α is *not* constant, meaning you find α(t) by differentiating ω(t), or recover ω by integrating α.

## Why It Matters

Angular acceleration lives in Topic 5.2, [Rotational Kinematics](/ap-physics-c-mechanics/key-terms/rotational-kinematics "fv-autolink"), and it's the variable that makes the rest of [Unit 5](/ap-physics-c-mechanics/unit-5 "fv-autolink") work. Rotational kinematics describes *how* something spins; rotational dynamics (torque and rotational inertia) explains *why*. The connection between the two is α. When an FRQ gives you a torque and a rotational inertia, α is what you solve for, and from α you get ω(t), θ(t), or the linear motion of a point on the object. Because Physics C is calculus-based, you're expected to handle α as a derivative of ω and as an integral target, not just plug into constant-acceleration equations. It also shows up in rolling-without-slipping setups, where the constraint a = Rα ties an object's linear acceleration to its angular acceleration.

## Connections

### Torque (Unit 5)

[Torque](/ap-physics-c-mechanics/unit-5/3-torque/study-guide/kQhoEJrKtYjpul5K "fv-autolink") is the cause; angular acceleration is the effect. Newton's second law for rotation, τ_net = Iα, is the single most-used rotation equation on the exam. Find the net torque, divide by rotational inertia, and you have α.

### [Linear Acceleration (Unit 1)](/ap-physics-c-mechanics/key-terms/linear-acceleration)

Angular acceleration is [linear acceleration](/ap-physics-c-mechanics/key-terms/linear-acceleration "fv-autolink")'s rotational twin. Every constant-acceleration kinematics equation you know has a rotational version with α in place of a, and a point on a rotating object has tangential acceleration a_t = rα. Master one set and you've mastered both.

### ω (Angular Velocity) (Unit 5)

α is literally the time [derivative](/ap-physics-c-mechanics/unit-1/2-displacement-velocity-and-acceleration/study-guide/robnlCwaanT6NImP "fv-autolink") of ω. On non-uniform rotation problems, differentiating ω(t) gives you α(t), and integrating α(t) gets you back to ω. This derivative-integral chain (θ → ω → α) is pure Physics C.

### [Rolling Without Slipping (Unit 5)](/ap-physics-c-mechanics/key-terms/rolling-without-slipping)

When a wheel rolls without slipping, the constraint a = Rα locks linear and angular acceleration together. This one equation lets you combine F_net = ma and τ_net = Iα into a single solvable system, which is a classic FRQ move.

## On the AP Exam

Angular acceleration is a workhorse on both sections. MCQs test whether you can read α off a graph of ω versus t (it's the slope), apply rotational kinematics equations, or rank angular accelerations using τ = Iα. On FRQs, α is usually the middle step of a multi-part problem. The 2021 FRQ Q3 had a nonuniform rod where you compute rotational inertia by integration, then use the torque from gravity to find the rod's angular acceleration. The 2022 FRQ Q3 featured a uniform disk on a frictionless axle, again leading to α through τ_net = Iα. The pattern to internalize is: find I (often by integration), find net torque, solve for α, then convert to linear quantities with a = rα if the problem asks about a point or an attached object. Watch your signs when the object is slowing down, and always work in radians.

## Angular Acceleration vs Tangential (linear) acceleration

Angular acceleration α describes the whole rotating object and is the same for every point on a rigid body, measured in rad/s². Tangential acceleration a_t = rα describes one specific point and depends on how far that point is from the axis, measured in m/s². Two points on the same spinning disk share one α but have different tangential accelerations. Also don't confuse a_t with centripetal acceleration (v²/r or ω²r), which exists even when α = 0.

## Key Takeaways

- Angular acceleration is defined as α = dω/dt, the time rate of change of angular velocity, with units of rad/s².
- Newton's second law for rotation, τ_net = Iα, is how you actually calculate α in most exam problems.
- Every point on a rigid rotating body has the same angular acceleration, but tangential acceleration a_t = rα varies with distance from the axis.
- When α is constant, the rotational kinematics equations mirror the linear ones exactly, with θ, ω, and α replacing x, v, and a.
- When α is not constant, use calculus: differentiate ω(t) to get α(t), or integrate α(t) to recover ω(t).
- For rolling without slipping, the constraint a = Rα links the object's linear and angular accelerations into one solvable system.

## FAQs

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

Angular acceleration (α) is the rate of change of angular velocity, α = dω/dt, measured in rad/s². It's the rotational analog of linear acceleration and is found from τ_net = Iα when torques act on an object.

### Is angular acceleration the same for every point on a rotating object?

Yes. On a rigid body, every point shares the same α (and the same ω). What changes from point to point is the tangential acceleration, a_t = rα, which grows with distance from the axis.

### How is angular acceleration different from centripetal acceleration?

Angular acceleration measures how the spin rate changes (rad/s²), while centripetal acceleration (ω²r) points toward the axis and exists even at constant spin. A disk rotating at steady ω has zero angular acceleration but nonzero centripetal acceleration at every point off the axis.

### Can angular acceleration be zero while angular velocity is not?

Yes. An object spinning at constant angular velocity has α = 0, just like a car cruising at constant speed has zero linear acceleration. Constant ω means no net torque, not no rotation.

### How do you find angular acceleration on an FRQ?

Usually by computing the net torque and the rotational inertia, then solving τ_net = Iα. The 2021 FRQ (nonuniform rod) and 2022 FRQ (uniform disk on an axle) both follow this pattern, often requiring you to find I by integration first.

## Related Study Guides

- [5.2 Rotational Kinematics](/ap-physics-c-mechanics/unit-5/rotational-kinematics/study-guide/Gsw0lqWOAjobUHG86ljB)

## Structured Data

```json
{"@context":"https://schema.org","@graph":[{"@type":"LearningResource","@id":"https://fiveable.me/ap-physics-c-mechanics/key-terms/angular-acceleration#resource","name":"Angular Acceleration — AP Physics C Mech Definition","url":"https://fiveable.me/ap-physics-c-mechanics/key-terms/angular-acceleration","learningResourceType":"Concept explainer","educationalLevel":"AP® / High School","about":{"@id":"https://fiveable.me/ap-physics-c-mechanics/key-terms/angular-acceleration#term"},"audience":{"@type":"EducationalAudience","educationalRole":"student"},"dateModified":"2026-06-11T00:50:28.781Z","isPartOf":{"@type":"Collection","name":"AP Physics C: Mechanics Key Terms","url":"https://fiveable.me/ap-physics-c-mechanics/key-terms"},"publisher":{"@type":"Organization","name":"Fiveable","url":"https://fiveable.me"}},{"@type":"DefinedTerm","@id":"https://fiveable.me/ap-physics-c-mechanics/key-terms/angular-acceleration#term","name":"Angular Acceleration","description":"Angular acceleration (α) is the rate of change of angular velocity with respect to time, α = dω/dt, measured in rad/s². It is the rotational analog of linear acceleration and connects directly to torque through Newton's second law for rotation, τ_net = Iα.","url":"https://fiveable.me/ap-physics-c-mechanics/key-terms/angular-acceleration","inDefinedTermSet":{"@type":"DefinedTermSet","name":"AP Physics C: Mechanics Key Terms","url":"https://fiveable.me/ap-physics-c-mechanics/key-terms"}},{"@type":"FAQPage","mainEntity":[{"@type":"Question","name":"What is angular acceleration in AP Physics C?","acceptedAnswer":{"@type":"Answer","text":"Angular acceleration (α) is the rate of change of angular velocity, α = dω/dt, measured in rad/s². It's the rotational analog of linear acceleration and is found from τ_net = Iα when torques act on an object."}},{"@type":"Question","name":"Is angular acceleration the same for every point on a rotating object?","acceptedAnswer":{"@type":"Answer","text":"Yes. On a rigid body, every point shares the same α (and the same ω). What changes from point to point is the tangential acceleration, a_t = rα, which grows with distance from the axis."}},{"@type":"Question","name":"How is angular acceleration different from centripetal acceleration?","acceptedAnswer":{"@type":"Answer","text":"Angular acceleration measures how the spin rate changes (rad/s²), while centripetal acceleration (ω²r) points toward the axis and exists even at constant spin. A disk rotating at steady ω has zero angular acceleration but nonzero centripetal acceleration at every point off the axis."}},{"@type":"Question","name":"Can angular acceleration be zero while angular velocity is not?","acceptedAnswer":{"@type":"Answer","text":"Yes. An object spinning at constant angular velocity has α = 0, just like a car cruising at constant speed has zero linear acceleration. Constant ω means no net torque, not no rotation."}},{"@type":"Question","name":"How do you find angular acceleration on an FRQ?","acceptedAnswer":{"@type":"Answer","text":"Usually by computing the net torque and the rotational inertia, then solving τ_net = Iα. The 2021 FRQ (nonuniform rod) and 2022 FRQ (uniform disk on an axle) both follow this pattern, often requiring you to find I by integration first."}}]},{"@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"name":"AP Physics C: Mechanics","item":"https://fiveable.me/ap-physics-c-mechanics"},{"@type":"ListItem","position":2,"name":"Key Terms","item":"https://fiveable.me/ap-physics-c-mechanics/key-terms"},{"@type":"ListItem","position":3,"name":"Unit 5","item":"https://fiveable.me/ap-physics-c-mechanics/unit-5"},{"@type":"ListItem","position":4,"name":"Angular Acceleration"}]}]}
```