The **centripetal acceleration** , is the property of the **movement** that has a body that traverses a **circular path** . The acceleration is directed radially toward the center of the circle and has a **magnitude** equal to the square of the velocity of the body along the curve divided by the distance from the center of the circle to the moving body. The force causing this **acceleration** is also directed toward the center of the **circle** and is called the **centripetal** force .

**Unit:**m / s²**Formula:**a_{c = v 2 / r}

## What is centripetal acceleration?

Centripetal acceleration or **normal acceleration** is the acceleration that determines the **change** of **direction** in velocity in bodies rotating or moving around **curves** . It is called centripetal because it is always directed towards the **center of rotation** .

The centripetal acceleration is the idea that any object moving on a **circle** , in a circular motion, will have a **vector** of **acceleration** pointing **center** of that circle. This is true even if the object is moving around the circle at a **constant speed** . It is also important to know that the word centripetal means towards the **center** .

- What is centripetal acceleration?
- Formula
- As measured
- What is the direction of the centripetal acceleration
- Importance
- Examples

## What is centripetal acceleration?

It is the **magnitude** which is related to the change that occurs in the **direction** of the **speed** of a body which moves along a **path** of type **curvilinear** . Before this trajectory, the centripetal acceleration is directed to the center of the curve of the route.

It should be taken into account that when an object moves in a curved way, its speed will always undergo some **modifications** in terms of **direction** , regardless of whether the **speed** is constant. This is because the direction, beyond the speed, can never be **constant** .

A body can achieve a **uniform circular motion** and maintain constant speed while at the same time making a circular path. Although the speed remains constant, its speed is not because it is a magnitude that is tangent to the trajectory, and it changes its direction repeatedly while making the **circle** .

Centripetal acceleration, therefore, does not change the **speed** , but it does disturb its **direction** , allowing the development of the **trajectory** .

Centripetal acceleration is a type of acceleration that is always present and that is the cause that the **tangential velocity** , which is located in the part of the contour of the circumference, manages to suddenly change **direction** and **direction** , although it does not manage to have no influence on its **value** .

## Formula

The formula used to determine the centripetal acceleration of a given object can be calculated as the **tangential velocity** to the **square** of the **radius** or as follows:

**a**_{c = v 2 / r}**a**_{c}= v * ω

Where:

**a**= is the centripetal acceleration [m / s2]_{c}**v**= refers to the tangential velocity [m / s]**r**= is the radius of gyration [m]**ω**= is the angular velocity that is equal to 2 π f [rad / s]

## As measured

Centripetal acceleration can be measured in **m / s²** or in other words meters per second every second.

Since the force of the centripetal acceleration is inversely proportional to the square of the distance, the force will decrease by **2² = four times** . Being the force proportional to the product of the masses, when doubling one of them, the force will **double** .

The magnitude that represents the gravitational field intensity is the **acceleration of gravity** . For a mass m, relative to the mass M of the earth is g = F / m = G · M / R², where G is the universal gravitational constant.

## What is the direction of the centripetal acceleration

The bodies that present a **circular** motion always have centripetal acceleration, since the direction of the velocity changes with time. This acceleration has a type of **radial direction** and towards the **center** of the circumference that it describes. As generally such acceleration is perpendicular to the **tangential velocity** .

This being the case, we can say that the centripetal acceleration will always be found pointing towards the center of the circle according to **Newton’s** second **Law** .

## Importance

Centripetal acceleration is a very important movement because it is responsible for the **trajectory of** a mobile being a **circumference** .

## Examples

Some examples of centripetal acceleration are as follows:

- A ball at the end of the string rotates uniformly in a circle that has a radius of 0.60. The ball makes 2.0 revolutions per second. What is its centripetal acceleration?
- When you turn a corner in the car and the steering wheel is held stable during the turn with constant speed, you move in a uniform circular motion. A sideways acceleration is then observed because the person driving and the car change direction. The tighter the curve and the faster the speed, the more noticeable the acceleration.