OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
Centripetal force: (i) centripetal force; F = mv²/r; F = mω²r
Centripetal force is the resultant force that keeps a body moving in a circular path.
Checked against the OCR H556 specification (opens in a new tab) on .
- Point 4 of 4
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Centripetal force is the resultant force that keeps a body moving in a circular path. It acts towards the centre of the circle, perpendicular to the body's velocity, and changes the direction of motion without changing speed. By Newton's second law, F = ma, and substituting the centripetal acceleration gives F = mv²/r. Since v = ωr, substituting gives F = m(ωr)²/r = mω²r, so F = mω²r. For example, a 0.20 kg mass moving at 3.0 m s⁻¹ on a 0.60 m radius needs F = 0.20 × (3.0)²/0.60 = 3.0 N towards the centre. The force is provided by a real interaction such as tension, friction or gravity, not by a new outward force.
What earns the marks
- States that centripetal force is the resultant force directed towards the centre of the circular path.
- Applies F = mv²/r correctly, using mass in kg, speed in m s⁻¹ and radius in m to obtain force in N.
- Applies F = mω²r correctly, using ω in rad s⁻¹ and r in m to obtain force in N.
- Explains that the centripetal force is provided by a real force such as tension, friction or gravitational attraction.
- Links the two forms through v = ωr, showing F = mv²/r and F = mω²r are equivalent.
Common mistakes and how to put them right
Inventing an outward centrifugal force as the reaction to the centripetal force.
Put it right by stating that the centripetal force is the resultant inward force and any outward sensation arises from inertia.
Using diameter instead of radius in F = mv²/r.
Put it right by halving the diameter before substituting.
Forgetting to square the speed or angular speed.
Put it right by checking the exponent in the equation before calculating.
Using ω in rev s⁻¹ rather than rad s⁻¹.
Put it right by multiplying revolutions per second by 2π.
Exam tips
- Identify which real force supplies the centripetal force before substituting numbers, as questions often ask for this explanation.
- Choose F = mv²/r when speed is given and F = mω²r when angular speed or period is given.
- Check that the final force is quoted with a direction towards the centre when the question asks for a vector.
Try the lesson
The start of the Centripetal force: (i) centripetal force; F = mv²/r; F = mω²r lesson, made from checked teaching notes for this specification point.
Listen
Centripetal force is the resultant force that keeps a body moving in a circular path. It acts towards the centre of the circle, perpendicular to the body's velocity, and changes the direction of motion without changing speed. By Newton's second law, F = ma, and substituting the centripetal acceleration gives F = mv²/r. Since v = ωr, substituting gives F = m(ωr)²/r = mω²r, so F = mω²r. For example, a 0.20 kg mass moving at 3.0 m s⁻¹ on a 0.60 m radius needs F = 0.20 × (3.0)²/0.60 = 3.0 N towards the centre. The force is provided by a real interaction such as tension, friction or gravity, not by a new outward force. A strong answer earns marks for these points. States that centripetal force is the resultant force directed towards the centre of the circular path. Applies F = mv²/r correctly, using mass in kg, speed in m s⁻¹ and radius in m to obtain force in N. Applies F = mω²r correctly, using ω in rad s⁻¹ and r in m to obtain force in N. Explains that the centripetal force is provided by a real force such as tension, friction or gravitational attraction. A common slip: Inventing an outward centrifugal force as the reaction to the centripetal force. Instead, stating that the centripetal force is the resultant inward force and any outward sensation arises from inertia. Exam tip: Identify which real force supplies the centripetal force before substituting numbers, as questions often ask for this explanation.
See it
Key words
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Centripetal force
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Newton's second law in circular motion
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Real forces providing circular motion
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Relationship between linear and angular quantities
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See every definition
- Centripetal force
- The resultant force that keeps a body moving in a circular path, acting towards the centre of the circle and perpendicular to the body's velocity.
- Newton's second law in circular motion
- F = ma, and substituting the centripetal acceleration gives F = mv²/r.
- Real forces providing circular motion
- The force is provided by a real interaction such as tension, friction or gravity, not by a new outward force.
- Relationship between linear and angular quantities
- Since v = ωr, substituting gives F = m(ωr)²/r = mω²r, so F = mω²r.
Label the diagram
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