Practice
Circular motion
Centripetal acceleration, speed from the period, the force a string supplies, the slowest speed at the top of a loop and the fastest on a flat curve.
The skill
Circular motion is Newton's second law with the acceleration pointed at the center, . Draw the real forces, then ask which of them, or which components, point toward the center; their sum is . Static friction on a flat curve, or gravity alone at the top of a loop at the minimum speed, can play that role. Centripetal force is never an extra arrow on the diagram, and drawing one is the mistake to avoid. For uniform circular motion, the period links speed to the size of the circle through .
A worked example
A car rounds a flat, unbanked curve of radius 115 m. The coefficient of static friction between the tires and the road is 0.42. Use g = 10 m/s².
What is the greatest speed at which the car can round the curve without sliding, in m/s? Give your answer to three significant figures.
Solution
- Static friction toward the center is the only horizontal force, so it supplies the centripetal force. At the greatest speed it is at its maximum, μₛFₙ = μₛmg.
- μₛmg = mv²/r, so v = √(μₛgr) = √((0.42)(10)(115)) = 22.0 m/s.
Answer: 22