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=rmv2F=mω2rF=mωv
Centripetal acceleration
a=rv2a=ω2ra=ωv
VARIABLE DEFINITIONS
QUANTITY NAME
SYMBOL
DERIVED UNIT
SI UNIT
mass
m
kg
kg
radius
r
m
m
linearvelocity
v
ms−1
ms−1
angularvelocity
ω
rads−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=ma the equations for centripetal force can be derived from the equations for centripetal acceleration:
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.
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 1.50×1011m. The centripetal force on the Earth is 3.56×1022Nand the mass of the Earth is 5.97×1024kg.
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=1.50×1011mF=3.56×1022Nm=5.97×1024kg
Next, write down the equations needed and rearrange if necessary:
F=rmv2→v=mFr
Then, substitute the values into the equation:
v=5.97×10243.56×1022×1.50×1011v=29832.87...
Make sure to include units and round to the lowest number of significant figures of the values given by the question:
linearvelocity,v=29800ms−1
The linear velocity of the Earth as it orbits the Sun is 29800ms−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.