Banked Curves
Banking uses the normal force to supply centripetal force.
About this topic
On a banked curve, the road is tilted so that the normal force has a horizontal component pointing toward the centre of the turn, supplying some or all of the centripetal force without relying on friction. At the ideal speed, tan θ = v²/(rg).
Racetracks, railways and cycling velodromes all use banking, as do aircraft that tilt their wings to turn. On a flat road, only friction between the tyres and road keeps a car turning, so ice or rain can make the car skid straight on. Banking means the road itself does the job, giving a safer turn at higher speed.
Worked example: a curve of radius 100 m designed for 20 m/s needs tan θ = 400 / (100 × 9.8) ≈ 0.41, so θ ≈ 22 degrees. Driving slower than the design speed means the car tends to slide down the slope unless friction helps, and faster means it tends to slide up and outward.
Engineers make motorway bends banked slightly and use steeper banks on racetracks like Daytona, where angles reach about 31 degrees. A misconception is that a centrifugal force pushes the car outward; in the ground frame the only forces are gravity, normal and friction, and the car simply wants to continue in a straight line. The net inward force makes it turn.
Key ideas
- tan θ = v²/(rg) with no friction
- Faster curves need steeper banks
- Roads and tracks use banking
Quick check
Use cases: where Banked Curves helps
- Homework: review the key idea behind Banked Curves before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Banked Curves without notes.
- Visual learning: play with the interactive lab to see how Banked Curves changes when you adjust its inputs.
- Teaching a friend: explain Banked Curves in your own words, then compare your version with the key ideas.
The same laws describe car crashes, sports, satellites and everyday machines.
Frequently asked questions
What is Banked Curves?
Banking uses the normal force to supply centripetal force.
What will I learn in Banked Curves?
tan θ = v²/(rg) with no friction. Faster curves need steeper banks. Roads and tracks use banking.
Is Banked Curves part of Physics?
Yes. It is one of 150 Physics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Banked Curves lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Banked Curves?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.