Centripetal Acceleration

Centripetal Acceleration, also known as the Radial Acceleration, is the body’s acceleration that performs a circular motion around the centre of the circle. One of the key factors of Centripetal Acceleration is velocity, which is a vector quantity. The centripetal acceleration definition represents that the motion depends on the velocity of the molecules. The most important motions that satisfy the centripetal acceleration definition are uniform circular motion, motion under gravity and projectile motion. The motions have a constant magnitude but a continuous change in the direction is known as the uniform circular motion. The motion has a constant direction and a variable magnitude is called the motion under gravity. The motion whose direction and magnitude change constantly is called the projectile motion.

Characteristics and Properties of Centripetal Acceleration

According to the centripetal acceleration definition, it can be said that the Centripetal Acceleration has different characteristics. The characteristics of the Centripetal Acceleration are as follows.

• As per the centripetal acceleration formula, the centripetal acceleration always moves toward the circular path’s centre.

• Any type of particle’s acceleration under centripetal acceleration will be performed in a circular motion along the circle’s radius.

• There will be a continuous change in the direction during a centripetal acceleration.

• The magnitude of the centripetal acceleration has a linear acceleration.

The magnitude  of the Centripetal force depends on-

1. The velocity,

2. The distance of the object from the circular motion’s centre, and

3. The object’s mass

Centripetal Acceleration Formula

An object will not move if there is no centripetal force and if the object has a proper motion in its particles, it will be able to travel in a centripetal motion. Moreover, if the force is imbalanced, the particle of that object will remain in the same position. The centripetal acceleration formula is allocated to calculate the centripetal force from the speed of the body and the radius of the circular motion. The Centripetal Acceleration Formula is as follows: a_c = v²/r where the ‘v’ denotes the speed of the particles, ‘r’ represents the distance between the centre and the moving body. The centripetal force is calculated through this standard form of equation and it can be derived in two ways. The derivation of the Centripetal Acceleration formula can be presented through geometrical or calculus methods.

Derivation of Centripetal Acceleration Formula

The formula of centripetal acceleration can be derived from the centripetal acceleration definition depending on the velocity of the particles. The expression can be represented in the standard form of the Derivation of Centripetal Acceleration formula. The direction of the acceleration is toward the circular motion’s centre and the centripetal acceleration will be affected by the circular path. The centripetal acceleration and the radius vector create a centripetal angle whose mathematical value is 180°. The Derivation of Centripetal Acceleration can be done by various methods such as the geometric method, and calculus method. The Derivation of Centripetal Acceleration through the geometric methods means the projection of the equation from a geometric diagram of the centripetal motion of particles. The distance between the moving body and centre is taken and with the help of the speed of the particles, the standard equation is formed.

Conclusion

The study is based on the centripetal force and it gives some brief knowledge about the centripetal acceleration. The centripetal acceleration has a very important role in student life. The students who are studying the parts of physics or mechanics feel the importance of the centripetal force. The centripetal force also has importance in real life and it takes place from spinning a ball to the earth’s movement around the sun. The planets are moving around the sun and are not getting distracted from its path of circular motion only because of the involvement of gravitational force and the centripetal force.