IntermediateTopic 41 of 106Engineering Mechanics
Circular motion and centripetal force
Moving on a circle requires inward acceleration v²/r.
In depth
Uniform circular motion has acceleration a=v²/r=ω²r toward the centre, requiring a centripetal force F=mv²/r supplied by tension, friction, gravity or normal force. "Centrifugal force" is an apparent force in the rotating frame.
Key points
- Direction changes while speed is constant
- Maximum speed on a flat curve v=√(μgr)
- Period T=2πr/v
ExampleA 1000 kg car at 15 m/s on a 50 m curve needs 4.5 kN of friction.
Circular motion needs an inward force, and this principle is used in curves, centrifuges and orbiting systems.
What is Circular motion and centripetal force?
Moving on a circle requires inward acceleration v²/r.
Why is it important to understand circular motion and centripetal force?
Circular motion needs an inward force, and this principle is used in curves, centrifuges and orbiting systems.
Is centrifugal force a real force?
In the rotating frame it appears as a fictitious force. In the inertial frame, only the inward centripetal force acts, which is the real force needed to curve the path.
What does the centripetal acceleration depend on?
It equals speed squared over the radius, so doubling the speed quadruples the required inward force.
How is Circular motion and centripetal force used in practice?
Typical applications include designing the speed limit on a curve of a racetrack, sizing the bearing that holds a rotating arm and estimating the force on a rider on a loop-the-loop ride.
What should I learn before Circular motion and centripetal force?
Study "Rolling motion" first (topic 40 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
What are the key points of Circular motion and centripetal force?
Direction changes while speed is constant. Maximum speed on a flat curve v=√(μgr). Period T=2πr/v.
Can you give an example of Circular motion and centripetal force?
A 1000 kg car at 15 m/s on a 50 m curve needs 4.5 kN of friction.
What comes after Circular motion and centripetal force?
The next topic is "Banked curves", which builds directly on this one.
How difficult is Circular motion and centripetal force?
It is classed as Intermediate in Engineering Mechanics (topic 41 of 106). It is an intermediate topic. Work through the beginner topics in Engineering Mechanics first.