Mechanics

# Centripetal acceleration Examples

The acceleration that controls the change in direction of motion in rotating or curving bodies is known as the centripetal acceleration or normal acceleration. Since it constantly faces the center of rotation, it is known as centripetal.

The concept of centripetal acceleration states that any item traveling in a circle will have an acceleration vector pointing in the direction of the circle’s center. Even if the object is circling the circle at a constant speed, this is still true. Furthermore, it’s critical to understand that the definition of centripetal is “toward the center.”

## What is Centripetal acceleration?

It comprises the magnitude that is connected to the change in a body’s speed that occurs when it goes along a curvilinear-type route. The centripetal acceleration prior to this trajectory is focused on the route’s curve’s center.

It must be remembered that even though an item moves at a constant speed, a change in direction in its speed always occurs when it goes in a curved direction. This results from the fact that, in addition to speed, the direction can never be constant.

A body can move uniformly in a circle while keeping its speed constant and following a circular path.

The magnitude is tangent to the trajectory and changes its direction frequently while making the circle, thus even though the speed is constant, it is not constant.

Therefore, the development of the trajectory is made possible by the centripetal acceleration, which does not alter the velocity but does disturb its direction.

The tangential speed, which is located in the portion of the circumferential contour, manages to rapidly alter its direction and sense even if it does not manage to have any effect on its value due to the centripetal acceleration, a sort of acceleration that is constantly present.

Read also: Centripetal force Vs Centrifugal force

### Centripetal acceleration formula

The formula used to find out the centripetal acceleration of a given object can be calculated as the tangential velocity squared over the radius or as follows:

c = v 2 /r

c = v *ω

Where:

• c = is the centripetal acceleration [m/s2]
• v = refers to tangential speed [m/s]
• r = is the radius of gyration [m]
• ω = is the angular speed that is equal to 2 π f [rad/s]

### How is centripetal acceleration measured?

M/s2, or meters per second every second, can be used to determine centripetal acceleration.

The force will decrease by 22 = four times since the centripetal acceleration force is inversely proportional to the square of the distance. The force will double when one of the masses doubles since it is proportional to the product of the masses.

The acceleration due to gravity is the magnitude that symbolizes the strength of the gravitational field. In terms of a mass m in relation to the mass M of the earth, the formula is g = F/ m = G M / R2, where G is the gravitational constant of the universe.

### The direction of centripetal acceleration

Bodies that exhibit circular motion always have centripetal acceleration, since the direction of velocity changes with time. This acceleration has a type of radial direction towards the center of the circumference, it describes. Usually, this type of acceleration is perpendicular to the tangential velocity.

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

## Centripetal acceleration Examples in everyday life

Some examples of centripetal acceleration are as follows:

• A ball at the end of the string rotates uniformly in a circle of radius 0.60. The ball makes 2.0 revolutions per second. What is its centripetal acceleration?
• When the car is turned around a corner and the steering wheel is held steady during the turn at a constant speed, a uniform circular motion occurs. A sideways acceleration is then observed because the driver and the car change direction. The tighter the curve and the higher the speed, the more noticeable the acceleration.

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