---
title: "Radius — AP Physics 1 Definition & Exam Guide"
description: "Radius (r) is the distance from the center of a circle to its edge. In AP Physics 1, it drives centripetal acceleration, gravity (g = GM/r²), and torque."
canonical: "https://fiveable.me/ap-physics-1-revised/key-terms/radius"
type: "key-term"
subject: "AP Physics 1"
unit: "Unit 3"
---

# Radius — AP Physics 1 Definition & Exam Guide

## Definition

The radius (r) is the distance from the center of a circle or sphere to any point on its edge, equal to half the diameter. In AP Physics 1, r sets the size of a circular path and appears in centripetal acceleration (a = v²/r), gravitational field strength (g = GM/r²), torque, and angular momentum.

## What It Is

Geometrically, the radius is simple. It is the [distance](/ap-physics-1-revised/key-terms/distance "fv-autolink") from the center of a circle or sphere out to the edge, and it is half the diameter. In [AP Physics 1](/ap-physics-1-revised "fv-autolink"), though, radius is rarely just a shape measurement. It is the variable that controls almost everything about rotational and circular motion.

The same letter r shows up wearing different hats. In circular motion, r is the size of the path, and it sits in the denominator of a = v²/r. In gravitation, r is the distance from the center of a planet to the object, and it gets squared in g = GM/r². In rotation, r connects angular and linear quantities through v = rω, acts as the lever arm in [torque](/ap-physics-1-revised/unit-5/3-torque/study-guide/I9b5y8FshkMfALc5 "fv-autolink"), and appears in angular momentum (L = mvr for a point mass). Every time you see r, your first job is to identify what center it is measured from and what role it is playing in that equation.

## Why It Matters

Radius threads through Topics 3.4 ([Gravitational Field](/ap-physics-1-revised/key-terms/gravitational-field "fv-autolink")/Acceleration Due to Gravity on Different Planets), 3.6 ([Centripetal Acceleration](/ap-physics-1-revised/unit-2/9-circular-motion/study-guide/phypMTqBWYSyW4Xd "fv-autolink") and Centripetal Force), 7.3 (Angular Momentum and Torque), and 7.4 (Conservation of Angular Momentum). It also feeds energy reasoning under AP Physics 1 Revised 3.4.B, because gravitational potential energy and circular-motion kinetic energy both depend on how far an object sits from the center of its path or its planet. The exam loves r because it tests proportional reasoning. Double the orbital radius and gravitational field strength drops to one quarter. Double the radius of a circular path at the same speed and centripetal acceleration halves. If you can track how r scales through an equation, you can answer a huge slice of MCQs without a calculator.

## Connections

### Centripetal Acceleration and Centripetal Force (Unit 3)

In a = v²/r, the radius tells you how tight the turn is. A bigger radius at the same [speed](/ap-physics-1-revised/key-terms/speed "fv-autolink") means a gentler curve and less acceleration toward the center. Watch out though, because if angular speed ω is what stays constant instead, then a = ω²r and a bigger radius means MORE acceleration.

### [Acceleration due to gravity (Unit 3)](/ap-physics-1-revised/key-terms/acceleration-due-to-gravity)

In g = GM/r², the radius is the distance from the planet's center, and it gets squared. This is the inverse-square law in action. An object orbiting at twice Earth's radius feels one quarter the gravitational field. The 2018 FRQ about a spacecraft in a circular orbit of radius R is exactly this setup.

### Angular Momentum and Torque (Unit 7)

Radius is the [lever arm](/ap-physics-1-revised/key-terms/lever-arm "fv-autolink"). Torque grows with the distance from the axis where the force is applied, and angular momentum of a point mass is L = mvr. This is why an ice skater spins faster when she pulls her arms in. Shrinking r forces ω up to keep L conserved (Topic 7.4).

### Linear Velocity and Angular Velocity (Unit 7)

The equation v = rω is the bridge between rotational and linear motion. Two pulleys glued together on the same axle share one ω, but the point on the bigger [pulley](/ap-physics-1-revised/key-terms/pulley "fv-autolink") moves faster because its r is bigger. The 2021 short FRQ about two pulleys with different radii tests exactly this idea.

## On the AP Exam

Radius shows up constantly in released FRQs. The 2018 short answer put a spacecraft in a circular orbit of radius R around Earth and asked you to reason about its motion. The 2021 short FRQ attached two pulleys with different radii to a common axle, forcing you to use the fact that they share angular speed but not linear speed. The 2023 long FRQ spun a spring-mounted block in a circle, where the radius of the path itself changes as the spring stretches. In MCQs, expect proportional-reasoning stems like "if the radius doubles, the centripetal force becomes..." Your jobs are to (1) state what point r is measured from, (2) decide whether v or ω is held constant before predicting how a or F changes with r, and (3) square r correctly in gravitational field problems.

## Radius vs Altitude (height above the surface)

In gravitation and orbit problems, r is the distance from the planet's CENTER, not from the surface. A satellite at an altitude of one Earth radius is actually at r = 2R_Earth, so it feels g/4, not g/2. Plugging altitude into g = GM/r² instead of center-to-center distance is one of the most common point-killers on orbit questions.

## Key Takeaways

- Radius is the distance from the center of a circle or sphere to its edge, and it equals half the diameter.
- In gravitation, r is always measured from the planet's center, and field strength falls off as 1/r², so doubling the distance cuts g to one quarter.
- In centripetal motion, a = v²/r means a larger radius at constant speed gives a smaller acceleration, but a = ω²r means a larger radius at constant angular speed gives a larger one.
- The equation v = rω links rotation to linear motion, so points farther from the axis move faster even though everything shares the same angular velocity.
- Radius acts as the lever arm in torque and appears in angular momentum (L = mvr), which is why pulling mass closer to the axis makes a spinning object speed up.

## FAQs

### What is the radius in AP Physics 1?

It is the distance from the center of a circle or sphere to any point on its edge, half the diameter. On the exam it appears as the size of a circular path (a = v²/r), the distance from a planet's center (g = GM/r²), and the lever arm in torque and angular momentum.

### Is the orbital radius the same as the satellite's altitude?

No. Orbital radius is measured from the planet's center, so r equals the planet's radius plus the altitude. A satellite one Earth radius above the surface sits at r = 2R_Earth and experiences g/4.

### Does a bigger radius always mean more centripetal force?

No, it depends on what is held constant. With constant speed v, force shrinks as r grows (F = mv²/r). With constant angular speed ω, force grows with r (F = mω²r). Always check which quantity the problem fixes.

### How is radius different from diameter?

The diameter is the full distance across a circle through its center, and the radius is half of that. AP Physics 1 equations almost always use the radius, so if a problem hands you a diameter, divide by 2 before plugging in.

### Why do two pulleys attached to the same axle have different speeds at their edges?

They rotate together, so they share one angular speed ω, but linear speed is v = rω. The edge of the larger pulley moves faster because its r is bigger. The 2021 short FRQ tested exactly this with two pulleys of different radii on a common axle.

## Related Study Guides

- [Unit 3 FRQ (Circular Motion & Gravitation)](/ap-physics-1-revised/unit-Udr75ggSrboDhyB7/unit-3-frq-circular-motion-gravitation/study-guide/RFRmZgoHi2AwUw4p6gtm)
- [3.4 Gravitational Field/Acceleration Due to Gravity on Different Planets](/ap-physics-1-revised/unit-3/gravitational-fieldacceleration-due-gravity-on-different-planets/study-guide/Rw9bCoUwuOUFZLAo0o5E)

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