Centripetal Force Formula: Definition, Difference and Solved Examples

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The centripetal force formula gives the force acting on a body due to its circular motion around a fixed point.

A centripetal force is a force that causes a body to move in a circular motion.
The centripetal force always acts orthogonally to the motion of the body and towards the stationary point of the path's instantaneous center of curvature.
A common example of centripetal force is when a body moves at a constant speed along a circular path.
The centripetal force is exerted at right angles to the velocity as well as along the radius of the circular path towards the center.

The formula of centripetal force is given by

\(F_c=\frac{mv^2}{r}\)

Where

m is the mass of the body
v is the linear velocity of the body
r is the radius of the circular path

Table of Content

What is Centripetal Force?
Formula of Centripetal Force
Real-Life Examples of Centripetal Force
Difference between Centripetal and Centrifugal Force
Solved Examples
Things to Remember
Sample Questions

Key Terms: Force, Centripetal force, Centripetal acceleration, Linear velocity, Mass, Circular motion, Centrifugal force, Acceleration

What is Centripetal Force?

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The centripetal force acts on the object traveling in a circular direction and is directed towards the center upon which the object is moving.

When an object moves at a constant speed around a circular path, it encounters an accelerating centripetal force toward the center.
When we say centripetal, we are referring to the inclination to move towards the centre.
Centripetal refers to moving in a path that goes to the centre of something.

A centripetal force is defined as the force that makes any object move in a circular circle and assists it in remaining on the path. Additionally, three factors influence its worth:

The object's velocity as it travels along the circular path.
The distance between an object and the path's centre.
The object's mass.

Also Read:

Displacement vector	Centripetal Acceleration
Difference Between Scalar and Vector Quantities	Uniform Circular Motion

Formula of Centripetal Force

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The formula of centripetal force is given by

F_c= \(\frac{mv^2}{r}\)

Here,

F_c stands for the centripetal force
m stands for the mass of the object
v stands for the velocity of the moving object
r is the radius of the circular path

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Real-Life Examples of Centripetal Force

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Following are the Real-Life Examples of Centripetal Force:

Merry Go Rounds: A child is riding a merry-go-round in a disc that rotates. The youngster is in a condition of rest but is moving relative to the disk/wheel, which is rotating in a circular motion. In order to prevent the infant from being flung out, the centripetal force given by the support is sufficient.

Loops in Roller Coaster: The centripetal force, which seeks to maintain the roller coaster within the curvature along the track, helps the roller coaster accomplish such abrupt turns. For maximum centripetal acceleration during the corners, the turns are often not perfectly circular but shaped like a teardrop.

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Washing Machine Dryers: In our houses, this is the most prominent example of centripetal force. A washing machine's engine spins the drum at rapid speeds, causing the garments to spin at high velocities within the limited space. This will ensure that the clothing is cleaned more effectively. In a dryer, this will ensure that the clothes dry quickly. Because of the centripetal force, the clothing is not tossed out at random.

Banking in Roads: The banking technique entails elevating the road's edges to allow cars to turn safely. It is usually carried out in mountainous areas to avoid accidents; your angular momentum shifts in the other direction as you accelerate around the curves. A force is dragging the vehicle off the road. A force that pushes the car closer to the center is activated to counterbalance this force. The name given to this force is centripetal force.

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Dispersion in Prism	Electromagnetic Pulse	Physical Significance of Electric Field

Difference between Centripetal and Centrifugal Force

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Following are some Differences between Centripetal and Centrifugal Force:

Centripetal force	Centrifugal force
The centripetal force acts on the object traveling in a circular direction and is directed towards the center upon which the object is moving.	Centrifugal force emerges from the Inertia of a body in motion and is directed outwards from the body's axis of rotation.
Centripetal force originates from the gravitational pull and electrostatic force.	Centrifugal force originates from the Inertia of objects.
It is a real force acting on both inertial and non-inertial frames.	It is a pseudo force that acts in only inertial frames.
Formula is F_c=\(\frac{mv^2}{r}\)	Formula is F=mω²r
The direction of Centripetal force is from object to center.	The direction of the Centrifugal force is from center to object.
The centripetal force has the tendency to turn towards the center.	Centrifugal force has the tendency to move straight without having any turn.
Centripetal force makes us enter in a circular motion.	Centrifugal force makes us come out of circular motion.

Also Read:

The Principle of Homogeneity of Dimensions	Fundamental and Derived Units of Measurement
Path Length	Uniform Motion

Solved Examples

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Ques. A van of 1800 Kg travels at 60 m/s, and it covers a curve of 200 m. Then what is the value of the centripetal force?

Ans. The following are given:

m= 1800 Kg
r= 200 m
v= 60 m/s

Applying the formula of Centripetal force,

F_c = (1800×60×60) ÷200 = 32,400

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Ques. What is the Centripetal Force of a 180g ball that is tied to a pole with a 1.8 m rope and spins around the pole at 30 m/s?

Ans. The following are given:

m= 180 g = 180÷1000= 0.18kg
r= 1. 8m
v= 30 m/s

Applying the formula of Centripetal force,

F_c= (0.18×30×30) ÷1.8= 90 N.

Read More: Difference between AC and DC

Ques. Anita is gripping to the outer part of a 1.8-meter-diameter merry-go-round. Anita’s body weight is 40 kilograms, and the merry-go-speed round is 2.5 m/s. Calculate the Centripetal force.

Ans. Following are given:

d= 1.8, m= 40kg, r= 1.8 m, v=2.5m/s

r= ½ d= ½ ×1.8= 0.9 m

Applying the formula of Centripetal force,

F_c = (40×2.5×2.5) ÷0.9= 277.77 N

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Things to Remember

The centripetal force acts on objects moving towards circular motion.
Centripetal force is a real force that acts on both inertial and non-inertial frames.
The formula of the centripetal force is: F_c=\(\frac{mv^2}{r}\) .
Merry Go Rounds, and washing machine dryers are real-life examples of Centripetal force.

Also Read:

Newton's Universal Law of Gravitation and Gravitational Force	Conservation Laws in Physics
International Systems of Units	Measurement of Time

Sample Questions

Ques. Give a simple definition of Centripetal force. (2 Marks)

Ans. Centripetal force is a force that acts on the object traveling in a circular direction and is directed toward the center upon which the object is moving.

Ques. What is centripetal force? (2 Marks)

Ans. A centripetal force is a force that causes a body to move in a circular motion. The centripetal force always acts orthogonally to the motion of the body and towards the stationary point of the path's instantaneous center of curvature.

Ques. What is the direction of centripetal force? (1 Mark)

Ans. The direction of the centripetal force is toward the center of the circular path.

Ques. What is centrifugal force? (2 Marks)

Ans. Centrifugal force is an imaginary force that seems to be acting on a mass when observed from a circularly moving observer.

Ques. What is the direction of the centrifugal force? (1 Mark)

Ans. The centrifugal force is directed away from the center of the circular path (of the observer).

Ques. Define Centripetal Acceleration. (2 Marks)

Ans. Centripetal acceleration is the characteristic of the motion of an object that follows a circular path. Centripetal acceleration is based on the assumption that when an item moves in a circular motion, its acceleration vector will point to the center of the circle. Even if the item is traveling at a constant speed, this behavior will occur.

Ques. What is a Centrifuge? (2 Marks)

Ans. A centrifuge is a machine that separates or detaches things based on their density using centrifugal force. When a centrifuge spins, it generates a strong centrifugal force, which causes the contents to separate. The centrifuge machine produces quick results for laboratory and other purposes.

Ques. What is the dimensional formula of centripetal acceleration? (1 Mark)

Ans. The dimensional formula of centripetal acceleration is M⁰L¹T^-2.

Ques. Why does the increasing centripetal force not increase work? (3 Marks)

Ans. Because work and centripetal force do not have the same variables, increasing centripetal force does not increase work.

Because centripetal force = mv²/(r), where m=mass, v=velocity, and r=radius, and work = force * displacement. To have an effect on work, the centripetal force equation must be identical to the work equation, which is not conceivable.

Ques. Define force. (2 Marks)

Ans. A force is an effect that, unless counterbalanced by other forces, can cause an object's velocity to change, i.e., to accelerate.

Ques. On which factors does the Centripetal force depend? (3 Marks)

Ans. The following are the factors:

The velocity of the object as it travels along the circular path.
Distance between an object and the path's center.
Mass of the object.

Ques. Which force is responsible for Centripetal force? (2 Marks)

Ans. The frictional force is responsible for Centripetal force. The centripetal force is supplied by the frictional force, which is numerically equivalent to it. The centripetal force is orthogonal to velocity and results in a circular motion that is uniform.

Ques. What is the value of the centripetal forces acting on a 900 kg automobile traveling at 25.0 m/s around a 500 m radius curve? (3 Marks)

Ans. The following are given:

m= 900 Kg
r= 500 m
v= 25 m/s

Applying the formula of Centripetal force,

F_c = (900×25×25) ÷500=1125 N

Therefore, the Centripetal Force is 1125 (N).

Ques. Does speed impact the increase of Centripetal force? (2 Marks)

Ans. Yes, F_c= \(\frac{mv^2}{r}\), this formula denotes the centripetal force. It suggests that the increase in the speed of the object will also increase the centripetal force.

Ques. Does radius impact the increase of Centripetal force? (2 Marks)

Ans. No. F_c= \(\frac{mv^2}{r}\), formula denotes the centripetal force. It suggests that the increase of the radius of the turn of the object will decrease the centripetal force.

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Centripetal Force Formula: Definition, Difference and Solved Examples

What is Centripetal Force?

Formula of Centripetal Force

Real-Life Examples of Centripetal Force

Difference between Centripetal and Centrifugal Force

Solved Examples

Things to Remember

Sample Questions

CBSE CLASS XII Related Questions

1.
Draw the number of scattered particles versus the scattering angle graph for scattering of alpha particles by a thin foil. Write two important conclusions that can be drawn from this plot.

3.
Draw a circuit diagram of a full-wave rectifier using p-n junction diodes. Explain its working and show the input-output waveforms.

4.
Write the expression for the magnetic field due to a current element in vector form. Consider a 1 cm segment of a wire, centered at the origin, carrying a current of 10 A in positive x-direction. Calculate the magnetic field \( \mathbf{B} \) at a point \( (1 \, \text{m}, 1 \, \text{m}, 0) \).

5.
Two thin lenses of focal length \( f_1 \) and \( f_2 \) are placed in contact with each other coaxially. Prove that the focal length \( f \) of the combination is given by \[ f = \frac{f_1 f_2}{f_1 + f_2}. \]

6.
Suppose a pure Si crystal has \( 5 \times 10^{28} \) atoms per \( \text{m}^3 \). It is doped with \( 5 \times 10^{22} \) atoms per \( \text{m}^3 \) of Arsenic. Calculate majority and minority carrier concentration in the doped silicon. (Given: \( n_i = 1.5 \times 10^{16} \, \text{m}^{-3} \))

Comments

dOGVmW

Centripetal Force Formula: Definition, Difference and Solved Examples

What is Centripetal Force?

Formula of Centripetal Force

Real-Life Examples of Centripetal Force

Difference between Centripetal and Centrifugal Force

Solved Examples

Things to Remember

Sample Questions

CBSE CLASS XII Related Questions

1. Draw the number of scattered particles versus the scattering angle graph for scattering of alpha particles by a thin foil. Write two important conclusions that can be drawn from this plot.

3.Draw a circuit diagram of a full-wave rectifier using p-n junction diodes. Explain its working and show the input-output waveforms.

4.Write the expression for the magnetic field due to a current element in vector form. Consider a 1 cm segment of a wire, centered at the origin, carrying a current of 10 A in positive x-direction. Calculate the magnetic field \( \mathbf{B} \) at a point \( (1 \, \text{m}, 1 \, \text{m}, 0) \).

5.Two thin lenses of focal length \( f_1 \) and \( f_2 \) are placed in contact with each other coaxially. Prove that the focal length \( f \) of the combination is given by \[ f = \frac{f_1 f_2}{f_1 + f_2}. \]

6.Suppose a pure Si crystal has \( 5 \times 10^{28} \) atoms per \( \text{m}^3 \). It is doped with \( 5 \times 10^{22} \) atoms per \( \text{m}^3 \) of Arsenic. Calculate majority and minority carrier concentration in the doped silicon. (Given: \( n_i = 1.5 \times 10^{16} \, \text{m}^{-3} \))

Comments

dOGVmW

1.
Draw the number of scattered particles versus the scattering angle graph for scattering of alpha particles by a thin foil. Write two important conclusions that can be drawn from this plot.

3.
Draw a circuit diagram of a full-wave rectifier using p-n junction diodes. Explain its working and show the input-output waveforms.

4.
Write the expression for the magnetic field due to a current element in vector form. Consider a 1 cm segment of a wire, centered at the origin, carrying a current of 10 A in positive x-direction. Calculate the magnetic field \( \mathbf{B} \) at a point \( (1 \, \text{m}, 1 \, \text{m}, 0) \).

5.
Two thin lenses of focal length \( f_1 \) and \( f_2 \) are placed in contact with each other coaxially. Prove that the focal length \( f \) of the combination is given by \[ f = \frac{f_1 f_2}{f_1 + f_2}. \]

6.
Suppose a pure Si crystal has \( 5 \times 10^{28} \) atoms per \( \text{m}^3 \). It is doped with \( 5 \times 10^{22} \) atoms per \( \text{m}^3 \) of Arsenic. Calculate majority and minority carrier concentration in the doped silicon. (Given: \( n_i = 1.5 \times 10^{16} \, \text{m}^{-3} \))