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Centripetal force

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Summary

Centripetal Force

​​In a nutshell

Centripetal force can be any type of force that acts as a resultant force, keeping an object in circular motion. Centripetal force acts towards the centre of a circle. 


EQUATIONS

DESCRIPTION

EQUATION

Centripetal force
​F=mv2rF=mω2rF=mωvF=\frac {mv^2}{r} \newline \\[0.1in]F=m\omega^2 r\newline \\[0.1in]F= m\omega v \newline \\[0.1in]F=rmv2​F=mω2rF=mωv​​​​​

Centripetal acceleration
​a=v2ra=ω2ra=ωva = \frac{v^2}{r} \newline \\[0.1in]a=\omega^2 r \newline \\[0.1in]a = \omega va=rv2​a=ω2ra=ωv​​

VARIABLE DEFINITIONS


QUANTITY NAME

SYMBOL

DERIVED UNIT

SI UNIT

​massmassmass​​
​mmm​​
​kgkgkg​​
​kgkgkg​​
​radiusradiusradius​​
​rrr​​
​mmm​​
​mmm​​
​linear velocitylinear\ velocitylinear velocity​​
​vvv​​
​ms−1ms^{-1}ms−1​​
​ms−1ms^{-1}ms−1​​
​angular velocityangular\ velocityangular velocity​​
​ω\omegaω​​
​rads−1rads^{-1}rads−1​​
​rads−1rads^{-1}rads−1​​


Centripetal Force

Newton's first law of motion states that for an object to be accelerating, the must be a force acting on it. For circular motion, this force is called the centripetal force and is always directed towards the centre of the circle. 


Note: Centripetal force is not to be confused with centrifugal force. Centrifugal force isn't part of A level physics and you will lose credit in exam answers for mentioning it. So forget it for now.


Using Newton's second law of motion F=maF=maF=ma the equations for centripetal force can be derived from the equations for centripetal acceleration:


​F=m×(v2r)→F=mv2rF=m×(ω2r)→F=mω2rF=m×(ωv)→F=mωvF=m\times (\frac {v^2} {r}) \rightarrow F=\frac {mv^2}{r} \newline \\[0.1in]F=m\times (\omega^2 r) \rightarrow F=m\omega^2 r\newline \\[0.1in]F=m\times (\omega v) \rightarrow F= m\omega v \newline \\[0.1in]F=m×(rv2​)→F=rmv2​F=m×(ω2r)→F=mω2rF=m×(ωv)→F=mωv​​

The centripetal force can be any type of force which depends on the scenario.


Example

For the Earth orbiting the Sun, the centripetal force is provided by the gravitational force of the Sun.


Physics; Circular Motion; KS5 Year 12; Centripetal force
1
Velocity
2
Centripetal force


For an object on a string being swung around a persons head, the centripetal force is provided by the tension in the string.


​​Example

Calculate the linear velocity of the Earth as it orbits the Sun at a distance of 1.50×1011 m1.50 \times 10^{11} \, m1.50×1011m. The centripetal force on the Earth is 3.56×1022 N3.56\times 10^{22} \, N3.56×1022N and the mass of the Earth is 5.97×1024 kg5.97 \times 10^{24} \, kg5.97×1024kg.


Note: Some exam boards give the mass of the Earth in the booklet, make sure you double check before your exam. 


Firstly, write down the known values: 


r=1.50×1011 mF=3.56×1022 Nm=5.97×1024 kgr=1.50\times 10^{11} \, m \newline \\[0.1in]F=3.56\times 10^{22} \, N \newline \\[0.1in]m=5.97\times 10^{24} \, kgr=1.50×1011mF=3.56×1022Nm=5.97×1024kg


​Next, write down the equations needed and rearrange if necessary:


F=mv2r→v=FrmF=\frac {mv^2}{r} \rightarrow v=\sqrt {\frac {Fr}{m}}F=rmv2​→v=mFr​​


Then, substitute the values into the equation:


v=3.56×1022×1.50×10115.97×1024v=29832.87...v=\sqrt {\frac {3.56\times 10^{22} \times 1.50 \times 10^{11}}{5.97\times 10^{24}}} \newline \\[0.1in]v=29832.87...v=5.97×10243.56×1022×1.50×1011​​v=29832.87...


Make sure to include units and round to the lowest number of significant figures of the values given by the question:


linear velocity, v=29 800 ms−1linear \ velocity, \ v=29\,800\ ms^{-1}linear velocity, v=29800 ms−1​​​​​


The linear velocity of the Earth as it orbits the Sun is 29 800 ms−1‾.\underline{29\,800\ ms^{-1}}.29800 ms−1​.​

​

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FAQs - Frequently Asked Questions

What are some examples of centripetal force?

Some examples of centripetal force include the gravitational force between two celestial bodies, tension in a yo-yo string and the friction between a car's tyres and the road.

What is centripetal force?

Centripetal force is the resultant force that keeps an object in circular motion and it always acts towards the centre of a circle.

Where does centrifugal force come from?

Newton's first law of motion states that for an object to be accelerating, the must be a force acting on it.

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