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Sources of Centripetal Force
Centripetal force can be supplied by different contact or field forces, such as static friction on a level curve.
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Recommended for Class 11
Sources of Centripetal Force
19. Static Friction on a Level Curve
When a vehicle travels around a level curve, static friction between its tyres and the road supplies the inward force.
fs = mv² / r
Friction acts horizontally toward the centre.
Without sufficient friction, the vehicle cannot follow the required circular path.
In real driving, weather, tyre condition and road condition also matter; the ideal equation is not a safety-speed recommendation.
20. Maximum Speed on a Level Curve
The maximum available static friction is:
fmax = μs N
On a horizontal road:
N = mg
Therefore:
fmax = μs mg
At the limiting condition:
μs mg = mv² / r
Cancelling mass:
μs g = v²r
Therefore:
vmax = √(μs r g)
This is an ideal physics model, not a real-world speed guideline.
Exam Focus
Exam Focus
Important points
- F_c may be friction, tension, gravity or normal force
- Level curve: friction supplies F_c
- vmax = √(μ r g) on a level curve
Important formulas
- vmax = √(μ r g) on a level curve
Common Mistakes
Common Mistakes
- Mistake
Saying acceleration is zero because speed is constant.
- Mistake
Directing centripetal acceleration outward.
- Mistake
Directing velocity toward the centre.
- Mistake
Treating centripetal force as an additional force.
- Mistake
Using diameter instead of radius.
- Mistake
Forgetting the square of velocity.
- Mistake
Assuming friction always acts opposite to the vehicle’s forward motion.
- Mistake
Using N = mg on every banked surface.
- Mistake
Ignoring other radial forces.
- Mistake
Confusing centripetal and tangential acceleration.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
F_c may be friction, tension, gravity or normal force
Level curve: friction supplies F_c
vmax = √(μ r g) on a level curve
Centripetal force can be supplied by different contact or field forces, such as static friction on a level curve.
Fc may be friction, tension, gravity or normal force
- Definition
- Centripetal force can be supplied by different contact or field forces, such as static friction on a level curve.
- Formula
- F_c may be friction, tension, gravity or normal force
- Critical warning
- Saying acceleration is zero because speed is constant.
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