# Physics Lesson 7.1.4 - The Meaning of Centripetal Acceleration

Welcome to our Physics lesson on The Meaning of Centripetal Acceleration, this is the fourth lesson of our suite of physics lessons covering the topic of Kinematics of Rotational Motion, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

## The Meaning of Centripetal Acceleration

We stated earlier that even when the rotational motion is uniform, the object has not the same velocity because of the change in direction, despite velocity may have the same magnitude. Therefore, we can assign an acceleration to this type of motion which is not as the traditional acceleration which takes place when an object sppeds up or slows down, but only because the velocity vector changes direction and thus, the difference between two such vectors in two different instants is not zero. As a result, when this difference (change in velocity) is divided by the time interval Δt it occurs, we obtain a non-zero acceleration, whose vector is directed towards the centre of circle. This is the reason why it is called "centripetal acceleration" (in symbols, aC) and not because the object itself point towards the centre. Look at the figure.

We can write:

aC = v2-v1/∆t

Obviously, the magnitude of centripetal acceleration does not depend only on the magnitude of velocity itself, but also on the radius of curvature. This is because greater the radius, larger the circle and smoother the curve. This means arcs resemble more and more to straight lines. When radius of circle is so long that arcs become straight, we cannot speak for centripetal acceleration anymore as it exists only in rotational motion. As an example in this regard, we can mention objects moving at short distances on Earth surface. We consider such paths as linear, despite the fact that the Earth is a sphere.

Therefore, we calculate the magnitude of centripetal acceleration by the formula

aC = v2/r

The unit of centripetal acceleration is [m/s2] although it is an acceleration that occurs only in rotational motion. Therefore, centripetal acceleration acts as a bridge between linear and rotational quantities.

### Example 4

What is the centripetal acceleration of a human at rest on Earth surface if he is at equator? Take radius of Earth R = 6371 km.

### Solution 4

Since the object is at rest, the only velocity we can assign to it, is the velocity of Earth rotation around itself. However, it is more convenient to use the concept of speed instead of velocity here, as we can apply the equation

v = 2πR/T

where T = 24 h = 24 × 60 × 60 = 86400 s and R = 6371 km = 6 371 000 m. Therefore, we have

v = 2 × 3.14 × 6371000 m/86400 s
= 463 m/s

Therefore, centripetal acceleration of the person at equator is

aC = v2/r = 4632/6 371 000 = 0.03 m/s2

Compared to gravitational acceleration (g = 9.81 m/s2) this centripetal acceleration is very small and thus, it is often negligible during the calculations. This is the reason why it is rarely taken into consideration during the soultion of exercises.

You have reached the end of Physics lesson 7.1.4 The Meaning of Centripetal Acceleration. There are 4 lessons in this physics tutorial covering Kinematics of Rotational Motion, you can access all the lessons from this tutorial below.

## More Kinematics of Rotational Motion Lessons and Learning Resources

Rotation Learning Material
Tutorial IDPhysics Tutorial TitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
7.1Kinematics of Rotational Motion
Lesson IDPhysics Lesson TitleLessonVideo
Lesson
7.1.1Understanding Some Useful Quantities of Rotational Motion as a Background
7.1.2Kinematics of Uniform Circular Motion
7.1.3Uniformly Accelerated (Decelerated) Rotational Motion
7.1.4The Meaning of Centripetal Acceleration

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