# Centripetal Acceleration And Mass: 5 Facts You Should Know

The centripetal acceleration and mass though are the independent quantities; the acceleration of the object depends upon its mass and inertia of the body.

The mass is an invariable quantity and hence does not change when the object is in a centripetal motion. But, the centripetal acceleration and mass are still related to each other, as the force required to accelerate the object depends upon its mass majorly.

## Does mass affect centripetal acceleration?

The centripetal acceleration is directly dependent on the velocity of the object and inversely related to the radii of the circle.

Once a force is applied to the object to displace it from its initial position and travel along its way in a circular path, the momentum and the velocity of the object are maintained constant. The centripetal acceleration lies in the direction along the radius vector of the circular path.

## Why does mass not affect centripetal acceleration?

The centripetal acceleration of the object is independent of the mass of the object as it is constant.

The total work done by the object in a circular motion is actually negligible. The kinetic energy of the object is conserved in a process, and therefore the velocity of the body remains constant. Thus, the mass of the object does not affect the centripetal acceleration in any way.

The force that is applied to the object to give it a torque depends upon the mass and other configurations of the object. The torque is a force applied tangentially to the body of the object that accelerates the object in a circular motion about its axis.

## Why does mass is required to calculate centripetal acceleration?

The centripetal acceleration is constant for a given mass and the radius of the circular loop; hence it does not really depend upon the mass of the object.

The mass of the object determines the amount of force required to be applied to its body to displace. If less force is applied to the object, then the velocity of the object will be small, and accordingly, the centripetal acceleration of the object will be lowered.

If the amount of electrostatic force applied to the electron in a conduction belt is more, then the centripetal acceleration of the electron will be high. In the same way, if the magnetic force generated in a coil due to the current-carrying wire is more, then the number of revolutions of the small size motor will be more.

For bigger size motors, the revolutions per second will be less for the same amount of current as compared to the motor having small radii. This difference is because of the mass and the radius.

## How are centripetal acceleration and mass related?

The centripetal acceleration is inversely related to the mass of the object.

Though the mass of the object is not a variable quantity while the object is in centripetal motion, the initial velocity of the object does depend upon its mass which further determines the centripetal acceleration of the object in a circular motion.

The mass is said to be related because sufficient force has to be applied over it in response to its mass to accelerate it. If you maintain the constant force on all the objects having different masses, then you will notice that the object with less mass will accelerate at high speed as compared to the objects with high masses.

## How to calculate centripetal force from centripetal acceleration and mass?

The force on the object in a centripetal motion relies directly upon the centripetal acceleration and mass.

The centripetal force can be calculated from the centripetal acceleration and the mass is F=mα. Here, α is the centripetal acceleration, and m is the mass. It is obvious that, if the mass of the object is more, then more force is required to be applied to the object to displace it from its place.

The centripetal force applied to the object in a circular motion is calculated using the formula,

F=mv2/r

Here, F is a centripetal force,

m is a mass of the object,

v is the velocity of the object in a circular motion, and

r is a radius of the circular path.

The formula to find the centripetal acceleration from the velocity of the object is given as:

α =mv2/r

The centripetal acceleration depends upon the radii of the circle. That means, if the radius is small, the centripetal acceleration will be high, while for larger radii, the centripetal acceleration will be reduced. In such a case, more force has to be applied to keep the body accelerating at a required rate.

Hence, the centripetal force acting on the body in a centripetal motion can be calculated using only the mass and the centripetal acceleration of the object using an expression.

F=mα

Based on the object expression, we can say that the force on the object in a centripetal motion is directly dependent on its mass and the centripetal acceleration.

### What is the centripetal acceleration and force on the object having a mass of 5 kg and moving with a velocity of 20 m/s along the circle of radius 30 m?

Given: The mass of the object is, m =5 kg

The velocity of the object is, v =20 m/s

The radius of the circular path is, r =30 m

The centripetal acceleration of the object is found to be 0.67 m/s2

The expression to find the centripetal force acting on the object using the centripetal acceleration is,

F=α

Substituting the values in this equation, we get:

F=5 kg\times 0.67 m/s2=3.37N

The force applied on the object having 5kg of mass is 3.37 N. The force applied would have been increased if the mass of the object was more than 5 kg.

#### Conclusion

The centripetal acceleration is in response to the centripetal force acting inward. Hence, the direction of the linear velocity of the object varies that every short distance. The object starts accelerating only on the application of external force applied to its body. The amount of force required to apply on a given object relies upon the total mass of the object that is to be displaced.

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