Circular Motion
A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 5 practice questions.
Moving in a circle at constant speed is still accelerating, because the direction of the velocity keeps changing. The acceleration points toward the center with size v²/r. Something real has to supply that inward net force, mv²/r: a string, friction, gravity, or a normal force.
1. Velocity along, acceleration in
2. “Centripetal” isn’t a new force
Centripetal force is a job, not a new kind of force. Ask which real force points toward the center:
A ball on a string: tension. A car on a flat curve: static friction from the road. The Moon around Earth: gravity.
There is no outward “centrifugal” force on the free-body diagram. You feel thrown outward on a turn because your body tries to keep going straight while the car turns.
Since a = v²/r, doubling the speed makes the needed force four times as large.
3. Example, then try it
A 1200 kg car rounds a flat curve of radius 50 m at 10 m/s. How much friction must the road supply?
Fnet = mv²/r = (1200)(10²) ÷ 50 = 2400 N, pointing toward the center of the curve.
That is static friction: the tires grip without sliding sideways.
A 0.50 kg ball on a 0.80 m string is swung in a vertical circle. At the lowest point it moves at 4.0 m/s. Find the tension there. (g = 10 m/s²)
Center is straight up, so take up as + and the net force must point up.
Needed acceleration: a = v²/r = 16 ÷ 0.80 = 20 m/s² upward.
Forces: tension up, weight down: FT − mg = ma.
Solve: FT = m(g + a) = 0.50(10 + 20) = 15 N.
Answer: 15 N, three times the ball’s 5 N weight.
4. Common mistakes
A ball on a string moves in a horizontal circle. Suddenly the string breaks. Which way does the ball go?
Once the string breaks, nothing pulls it inward, so it keeps moving in a straight line in the direction it was going at that instant: along the tangent.
Ready to practice?
5 questions on Circular Motion, each with a hint and an explanation for every wrong answer.