Circular Motion & Gravitational Fields
An object moving in a circular path at constant speed is continuously changing direction, which requires a resultant centripetal force directed toward the centre of the circle. In A-Level Physics, combining circular motion equations with Newton's Law of Gravitation explains satellite orbits, angular speed, and planetary motion.
- Angular Velocity (ω)
- The rate of change of angular displacement, measured in radians per second (rad s⁻¹).
- Centripetal Acceleration
- The acceleration of an object moving in a circle, directed toward the center of the circle (a = v²/r or a = ω²r).
- Gravitational Field Strength (g)
- The gravitational force exerted per unit mass on a small object placed in the field (g = F/m).
Circular Motion & Gravitational Fields: Wave Equation (v = fλ) & Force Vector (F = ma) Simulator
Adjust physical variables on the sliders below to see real-time changes in wave geometry, resultant forces, and acceleration.
F_net = 80 N − 25 N = 55 NAcceleration: a = F_net ÷ m = 55 ÷ 10 = 5.50 m/s²Key Concepts & Exam Definitions (5)
- Angular Velocity (ω)
- The rate of change of angular displacement, measured in radians per second (rad s⁻¹).
- Centripetal Acceleration
- The acceleration of an object moving in a circle, directed toward the center of the circle (a = v²/r or a = ω²r).
- Gravitational Field Strength (g)
- The gravitational force exerted per unit mass on a small object placed in the field (g = F/m).
- Gravitational Potential (V)
- The work done per unit mass to move a small object from infinity to that point in the gravitational field.
- Geostationary Orbit
- An equatorial orbit with a time period of 24 hours, so a satellite stays above the same point on Earth's surface.
Quick-Fire Flashcards (5)
Click any card to check the answer, then mark it as Known to track your progress.
What provides the centripetal force for a car cornering on a flat road?
How is angular velocity (ω) related to time period (T)?
What is the relationship between gravitational force and distance (r)?
Why is gravitational potential always negative?
What is escape velocity?
Exam-Style Questions & Mark Schemes (3)
Write or think through your answer first, then click Check Mark Scheme to see the exact points examiners award marks for.
- Q1
A satellite orbits the Earth. Show that the time period T of the orbit is proportional to r^(3/2), where r is the orbital radius.
Click “Check Mark Scheme” to compare your answer, The centripetal force is provided by the gravitational force: mv²/r = GMm/r². Simplifying gives v² = GM/r. Since v = 2πr/T, then (2πr/T)² = GM/r. Expanding: 4π²r²/T² = GM/r. Rearranging for T² gives T² = (4π²/GM)r³. Therefore, T ∝ r^(3/2).
- Q2
Explain why a person on a Ferris wheel feels "heavier" at the bottom of the ride.
Click “Check Mark Scheme” to compare your answer, At the bottom, the centripetal force is directed upwards toward the center. The resultant force F = Normal reaction (R) - Weight (mg) = mv²/r. Therefore, R = mg + mv²/r. The normal reaction R is the force the seat exerts on the person, which is what they feel as their "apparent weight." Since R > mg, they feel heavier.
- Q3
Define gravitational potential and explain how it relates to work done when moving a mass.
Click “Check Mark Scheme” to compare your answer, Gravitational potential at a point is the work done per unit mass in bringing a test mass from infinity to that point. Work done on a mass m moving between two points with a potential difference ΔV is calculated by W = mΔV.
Common Exam Questions (3)
What is centripetal force?
Centripetal force is not a separate type of force; it is the resultant force (provided by tension, gravity, friction, or normal contact force) acting perpendicular to an object's velocity toward the centre of its circular path.
Why does an object in uniform circular motion accelerate if its speed is constant?
Velocity is a vector quantity with both magnitude (speed) and direction. Because an object in circular motion continuously changes direction, its velocity is continuously changing, which by definition means it is accelerating toward the centre of the circle.
What is Newton's Law of Universal Gravitation?
Newton's Law of Universal Gravitation states that every point mass attracts every other point mass with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres: F = Gm₁m₂ / r².
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