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Wize AP Physics C: Mechanics Textbook > Unit 2: Newton's Laws of Motion (17-23%)

Banked Roads

Centripetal Acceleration and Centripetal ForcePrevious Section
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Car Turning Around a Circular Section of Road



  • If the road is flat, then the centripetal force is equal to the force of friction on the car.
  • If there is no friction, there is no force that can supply the centripetal force required to make the car move in a circular path - there is no way that the car can turn!
  • If the road is banked, the horizontal component of the normal force provides the centripetal force.


Wize Concept
If a car is turning around a curve without friction, then the curve must be banked at some angle θ\theta(in radians) in order for the car to not slide out of the turn.





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Example: Car in a Flat Ramp


A car is negotiating a 160160 m diameter flat ramp and is about to slip off the road with speed of 9090 km/h. What is the coefficient of static friction between the tires and the road?

A) 0.80.8 B) 0.60.6 C) 0.40.4 D) 0.150.15



First, let's convert the speed: 90 kmhr=90⋅1000 m3600 s=25 ms90 \ \dfrac{km}{hr}=90\cdot\dfrac{1000\ m}{3600\ s}=25\ \dfrac{m}{s}

The only force toward the centre of this circular path is the static friction between tires and the road.

Since the car is about to slip off, it means that we are talking about the maximum static friction (the car is on the verge of sliding).

So, the centripetal force is equal to maximum static friction:


Horizontal direction: ∑F=mac\sum F=ma_c

Fstatic, max=mv2rF_{static, \ max}=\dfrac{mv^2}{r}
μsN=mv2r\mu_sN=\dfrac{mv^2}{r}

Vertical direction: ∑F=0\sum F=0 since there is no motion along this direction
NB−mg=0N_B-mg=0
N=mgN=mg

Combining the equations we get:

μsmg=mv2r\mu_s\cancel mg=\dfrac{\cancel mv^2}{r}

μs=v2rg\mu_s=\dfrac{v^2}{rg}

=25280×9.81=0.8=\dfrac{25^2}{80\times9.81}=0.8


A racing car is moving on a circular banked track with radius of 200200 m at a constant speed. The driver feels a normal force 3030 percent heavier than his true weight. What are the angle of the bank and the speed of the racing car?