Centripetal Force

Introduction:

The stamina, power, energy, or potency as an aspect of physical action or movement is called force. In other words, any push or pull upon an object resulting in its movement is forced. A force has both magnitude and direction, therefore, making it a vector quantity.

Force is represented as F and its SI unit is Newton.

Force is given as the product of mass and acceleration because whenever a force is applied to any object it results in the object’s motion with its weight, therefore,

F=mass×acceleration

F=m×a

Now, if a force makes the body follow a curved path it is called Centripetal Force. For example, when a stone is tied to a thread and we swing it, it follows a circular motion so the force which makes the body follow that circular motion is the Centripetal Force. It can also be said as the center seeking force.

In our day-to-day life, we use the term force and without realizing it we are using it while opening a door, riding a bicycle, lifting an object, etc. are the most common things we perform. A force is defined as the result of a physical action that causes the change in direction or motion of the object from the rest. In other words, any push or pull upon an object resulting in its movement is forced. A force has both magnitude and direction, therefore, making it a vector quantity. The centripetal force is defined as a force that acts on a body moving in a circular motion and is directed towards the centre. The word centripetal means center-seeking therefore, it is called center-seeking force. If you want to keep the body in a circular motion a force is needed to be exerted towards the center to compel the body to move in circular motion otherwise it will deviate from its path and attain linear motion. Few examples of centripetal force are planets moving around the sun, roller coasters, merry-go-round, etc.

Definition of Centripetal force:

When a body moves in a circular path, it experiences accelerated motion in its curved path which requires a force in its center of curvature path; this force is called Centripetal force. The object following this curved path due to centripetal force forms a circle and therefore moves in a circular motion with accelerated speed. Therefore, Centripetal force has magnitude and can be said center seeking force, it is represented as

F(centripetal)=m v² / r

Where,

F = force

v= tangential velocity in metres

And r = radius of the circular path in metres in which the object is moving.

Centripetal force can be understood with Newton’s first law of motion, the law of inertia. As the law states, “Any object in motion tends to be in motion with the same speed and the same direction unless disturbed by an unbalanced force”

Therefore, it’s a natural tendency of an object to continue to move with the same speed and direction unless disturbed by any other foreign force to deviate its direction from a straight line to make it turn. This presence of foreign force makes objects move in a circular motion. This force that causes uniform circular motion is called Centripetal force.

Calculation of Centripetal Force:

As seen above that the centripetal force is represented as

F=mv² / r

Hence, the force is measured in Newton (N).

We need to know the mass of an object, its tangential velocity, and its distance from the center. Because the force is represented as the square of velocity so if velocity doubles the force is quadruple. To calculate the velocity from the above expression:

F=mv² / r

Therefore,

v=(Fr / m)^1/2 m/s

Scientists have been using centripetal force for decades in their space programs to calculate the Earth orbit of a satellite. To keep the object moving at a fixed tangential velocity such that the gravitational force of the Earth at that distance is exactly equal to the centripetal force needed to keep the object in orbit is the idea of an Earth orbit.

Now, the gravitational force of Earth acting on a satellite is:

F(g)=3.986×10¹⁴ m / r²

If this gravitational force is equal to the centripetal force, then

m v ² / r=3.986×10¹⁴ m / r ²

Therefore,

v=1.996×10⁷ 1 / √r

Thus, the tangential velocity is independent of the mass of the satellite and to keep the satellite in orbit it is inversely proportional to the square root of the orbital radius.

Examples of Centripetal Force in daily life are as follows:

• 

  In solar system:

Planets in the solar system orbit around the sun, here centripetal force is equal to the gravitational force as we have seen above.

• A roller coaster ride:

Riding on the roller coaster we can feel the force and seats push you towards the center.

• Merry-go-round:

Everyone has experienced this in their childhood, once you start the merry-go-round it attains a certain speed in a circular motion and once you are riding on it the centripetal force of your feet with the metal doesn’t let you fly off and you enjoy the ride.

• 

  A car on circular track:

We have seen that when a car moves on a circular track then to move the car successfully in the circular direction it’s important that the car doesn’t skid off the road which is possible due to centripetal force between your car’s tyres and the road.

Also read: Work Done by a Constant Force

Frequently Asked Questions (FAQs):

Question 1: Centripetal Force is directed towards the center or outside the center?

Answer: Centripetal force is the force acting on an object moving in a circular path directed towards the center of the path.

Question 2: Difference between Centripetal Force and Centrifugal Force?

Answer: The main difference between the centripetal force and the centrifugal force is the frame of reference. Let’s take an example when a person is sitting on a roller coaster then he feels a force pushing him outside or someone is pulling him outward from his seat this force is centrifugal force and when we look at that person sitting on a roller coaster, we feel that something is pulling him towards the center so, the force which acts towards the center is called centripetal force.

Question 3: Any industrial application of centripetal force?

Answer: In automotive industries, centripetal force sensors are being used to sense the curving path during driving hence, increasing the driver’s safety.

Question 4: What is the SI unit of centripetal force?

Answer: The SI unit of Force is Newton(N) therefore, the S unit of centripetal force is also Newton(N).

Question 5: Why is centripetal force important for vehicles?

Answer: Centripetal force is important for a vehicle to take a turn. When a vehicle moves in a circular or sharp curve then the friction between the tyres and the road due to centripetal force prevents the vehicle from skidding off from the road.