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Physics

Centripetal Acceleration

The acceleration an object experiences when moving in a circular path, directed towards the center of the circle.

a_{c} = \frac{v ^{2}}{r}

Study tools

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Source & review

Difficulty

Intermediate

Read time

5 min

Prerequisites

Kinematics

Review statusNeeds review

Source

FormuLab initial formula library

Initial content draft pending verification against authoritative course or textbook sources.

Definition

Understanding the core concept

When an object moves in a circle, even if its speed is constant, its direction of motion is continuously changing. Since velocity is a vector (magnitude and direction), a change in direction means the velocity is changing, which implies an acceleration. This acceleration, known as centripetal acceleration, is always directed inwards towards the center of the circular path, ensuring the object stays on its curved trajectory rather than moving in a straight line.

Variables & Units

Understanding each component

Symbol	Meaning	Units
$a_{c}$	Centripetal acceleration	$m/s^{2}$
$v$	Tangential (linear) velocity of the object	$m/s$
$r$	Radius of the circular path	$m$

Real-World Applications

Where this formula is used in practice

Satellite Orbits

Explains why satellites remain in orbit around planets, as gravity provides the necessary centripetal acceleration.

Cars Turning

Describes the inward acceleration required for a car to make a turn on a road without skidding, provided by friction.

Amusement Park Rides

Applied in the design of rides like Ferris wheels and roller coasters to ensure safe circular motion for passengers.

Centrifuges

Used in laboratories and industry to separate substances by subjecting them to high centripetal acceleration.

Worked Example

Step-by-step calculation with real numbers

Problem

A car is moving at a constant speed around a circular track with a radius of 75 meters. If the car's speed is 15 meters per second, what is its centripetal acceleration?

Given

v = 15 m/s

r = 75 m

Solution

a_{c} = \frac{v ^{2}}{r}

a_{c} = \frac{( 15 m/s ) ^{2}}{75 m}

a_{c} = \frac{225 m ^{2} / s ^{2}}{75 m}

a_{c} = 3 m/s^{2}

Final Answer

a_{c} = 3 m/s^{2}

Formula Guide

Info

DifficultyIntermediate

Read Time5 min

PrerequisitesKinematics

Tools

Source & review

StatusNeeds review

Last reviewedPending

Source

FormuLab initial formula library

Initial content draft pending verification against authoritative course or textbook sources.

Assumptions

• Use SI units unless the formula or course context states otherwise.
• Check notation, sign conventions, and applicability against your course material.
• Confirm variables and assumptions before using the formula in graded or professional work.