What is Centripetal Force?

A particle, body, object or certain mass while travelling in a rotational path or semicircular path, experiences an inertia force. If that inertia force pulls the towards the inward of the imaginary circle in the rotation, it is termed as centripetal force.

Why is Centripetal Force called Center Seeking Force?

• If a vehicle is moving in a straight road at varying speed it is termed as the vehicle has accelerated in forward direction.
• If you apply brakes in your vehicle, the vehicle will jerk backwards, it means the vehicle has decelerated or retardation in backward direction.

We will come to our core part. When a vehicle takes a turn, what happens to the wheels? Will both travel at same speed? If both travel at the same motion of speed, no vehicle can take a turn in this world. This has kept the automobile industry stunned for a few decades. The important innovation of mechanical plays its own truant role here.

Differential gear, it will make the outer wheel experience centrifugal force pulling the car outward, whereas inline wheels experience centripetal force, pulling the car inwards of the imaginary turn circle. Since the car is pulled inward by the centripetal force it is termed as center seeking force. The inner wheel experiences a motion of centripetal force.  The outer wheel travels faster, inner wheel travels slower, so centripetal force at inline wheels pulls it inside and makes the wheels to travel slowly, the outer wheels are pulled outward by centrifugal force of motion, which makes the outer wheel to travel faster. So, both centripetal and centrifugal force nullify them equally in the reaction. How they nullify each other is discussed in forthcoming explanations.

Distinction between Centripetal and Centrifugal Force?

This centripetal and centrifugal force have kept humans amused in amusement parks all over the world. Starting from merry-go, giant wheel, roller coaster, rock-n-roll, human chain hanging everywhere, this simple physics of centripetal force and centrifugal force plays its dominant role.

Imagine a merry-go round. There are four children in four slots of a merry-go, one of the parents has spinned the merry- go faster. After spinning, if he leaves the merry-go he will fall in an inclined plane or imbalance in an inclined circular plane. The parent experiences the centrifugal force, so he is thrown outwards. The children inside the merry-go will experience an inward force that pulls them inward of the radius of the inside circle. They will be experiencing centripetal force. If any child tries to move a distance backward in the merry-go or put his head outwards by opposing the gravitational force, he will be thrown out in a circular path at some angular velocity, due to centrifugal force,

Centripetal force tries to keep it inwards, while centrifugal force keeps it outwards. They both are equal in magnitude and opposite in direction. They both are measured in newton.

Centripetal Acceleration

Angular velocity will have the same magnitude in different directions; hence velocity is a variable. When it comes to centripetal acceleration the magnitude remains the same but direction will continuously change in a circular path of constant radius. Centripetal acceleration is always perpendicular to velocity. Centripetal force is non-inertial if the body comes to rest at acceleration is zero.

Angular velocity – displacement / time = d/t

$\omega =\frac{\Delta \theta }{\Delta t}$

$\begin{array}{l}\omega \Delta t=\Delta \theta \\ \Delta \theta =\frac{\Delta v}{v}\\ \frac{\Delta v}{v}=\omega \Delta t\\ \frac{\Delta v}{\Delta t}=\omega v\\ v=\omega r\\ \frac{\Delta v}{\Delta t}=\omega v={\omega }^{2}r\end{array}$

$\Delta t\to 0$ r

Centripetal acceleration –  change in velocity / time

$a=\frac{\Delta v}{\Delta t}={\omega }^{2}r{\left(\frac{v}{r}\right)}^2=\frac{v^2}{r}$

The same reaction happens in centrifugal force in outwards manner ,it acts from opposite direction

$a=-\frac{v^2}{r}$

So they nullify each other. The velocity always acts tangential to the circle and perpendicular to acceleration.

Work by centripetal force

A centripetal force acting in a uniform circular motion will always change the direction of the object without changing the speed of the object.

The work done by centripetal force to change direction is force and displacement in the direction of the force changing

W = FORCE X DISPLACEMENT X cosθ

$w=f\times d\times \cos \theta$

Angle θ is the angle between the force and displacement, the normal force will move on in a uniform circular motion, the object will change its direction without changing its normal force. If it does so the centripetal work is acting on the system. Change of direction always happens in the horizontal direction of force hence it is taken as cosθ.

Newton's Law in Centripetal Force

Newton's first law

An object is said to have inertia, when it is disturbed from the rest or uniform motion. The centripetal force or center-seeking force will always move in uniform motion which exert inertia in the movement. Apply brakes to stop the vehicle from moving, hence inertia is brought to rest.

Newton's second law

The physics of an object always obeys Newton's second law f = ma . When an object is turning in a curve at constant acceleration, the force changes or depends on the mass of the object and acceleration of the object.

Newton's third law

Every action will have an equal and opposite reaction, if centripetal force pushes the object inwards, the centrifugal force will pull it outwards, hence it will nullify them.

It also obeys Newton's third law and has its own importance in Newtonian mechanics.

Centripetal Force Acting in Space

Although it is not the rotation revolution around the sun, the earth itself in which we live will experience a centripetal force, this is also called as pseudo-force or directional gravity which keeps earth in uniform motion. The earth is attracted inward towards the sun, the centripetal force acts from the earth to sun. The revolution of earth in its own orbit around the sun is due to the centripetal force of earth on an imaginary circular radius around the sun. The moon experiences the same centripetal effect as the sun experiences with the earth. Moon revolves around earth. The physics of space also has its milestone in centripetal force.

Centripetal Force in Real World  (Few Applications)

• A cycler bi-cycling in a circular track, bending downwards a little while turning the cycle.
• A biker while taking a sharp turn, will face centripetal force which acts as a friction to stop him from falling downwards. That’s why sometimes centripetal force is coined as pseudo-force.
• A jockey throwing rope at an animal to hunt. The rope maintains its inward circular shape due to centripetal force.
• Javelin throw is also a example of centripetal force
• Amusement park has many machines, which use rotational motion to amuse us. All rotational motion will be incidental by centripetal force.

Context and Applications  

This topic is significant in the professional exams for both undergraduate and graduate courses, especially for

• Bachelor of Science in Physics
• Master of Science in Physics