What is Circular Motion?
Circular motion happens when an object moves along a circular path at (often) constant speed. Even at constant speed, the object accelerates because its direction is always changing — this requires a centripetal force pointed toward the center.
In circular motion, an object needs a centripetal force F = mv²/r, directed toward the center of the circle, to keep it on its curved path — otherwise it would move in a straight line.
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Step-by-step worked examples
A 0.5 kg ball on a 1 m string spins at 4 m/s. Find the centripetal force.
F = m·v²/r F = 0.5 × 4² / 1 F = 0.5 × 16 / 1 F = 8 N
A 1000 kg car rounds a curve of radius 50 m at 20 m/s. Find the centripetal force needed.
F = m·v²/r F = 1000 × 20² / 50 F = 1000 × 400 / 50 F = 8000 N
A 500 kg satellite orbits at radius 7×10⁶ m with speed 7500 m/s. Find the centripetal force.
F = m·v²/r F = 500 × 7500² / (7×10⁶) F = 500 × 56,250,000 / 7,000,000 F ≈ 4017.9 N
Flashcards
Quick quiz
Q1.In circular motion, the centripetal force points…
Q2.What is the formula for centripetal force?
Q3.If speed doubles while mass and radius stay the same, centripetal force becomes…
Q4.What is the unit of centripetal acceleration?
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Common mistakes
Confusing centripetal force with 'centrifugal force' as if both are real. — Correct: Only centripetal force (inward) is real; centrifugal force is a fictitious effect felt in a rotating reference frame.
Thinking constant speed means no acceleration in circular motion. — Correct: Direction changes constantly, so there is always centripetal acceleration even at constant speed.
Using diameter instead of radius in the formula. — Correct: F = mv²/r requires the radius, not the diameter — dividing by diameter halves the correct force.
Forgetting that speed is squared in the formula. — Correct: Doubling speed quadruples the required force, not doubles it, because of the v² term.
FAQ
What is circular motion?
Motion along a circular path, where an object's direction constantly changes even if its speed stays constant.
What is the formula for centripetal force in circular motion?
F = mv²/r, where m is mass, v is speed, and r is the radius of the circular path.
How do you calculate centripetal force?
Square the speed, multiply by the mass, then divide by the radius: F = mv²/r.
What are examples of circular motion?
A car turning a curve, a satellite orbiting a planet, a spinning fairground ride, and a ball on a string are all circular motion.