# Banking on race track

## Homework Statement

Can anyone explain the above concept in a concise manner? I am proposing that banking aids motion at maximum speed on a curved surface. I am not totally sure how to include the role of side friction and centripetal force. Any further suggestions would be appreciated.

Another question relates to why at a certain speed a car experiences no sideways frictional force in a plane parrallel to the road surface. I am proposing that sideways friction induces circular motion in a car on a straight road. Since the plane is parallel to the road surface, the motion has to be linear. I am not sure how it relates to a certain speed.
Any suggestions? Thanks!

## The Attempt at a Solution

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No matter which way you look at it, it is circular motion. On a flat track, the radial component keeping the car going in a circle is the static friction force between the tire and the road (which is perpendicular/radial, not tangental to motion). As the banking of the track increases, the static frictional force still exists but decreases as the angle increases, and inversely, a normal force is introduced by the inward "contact" of the track. If the banking were completely vertical, there would be no more static friction force, and it would be 100% normal force. The circular motion formulas apply to all of these scenarios. The key thing to remember is that the centripetal force is equal to the sum of the radial components of all forces acting on the car.

I should add that the static friction force is limited by the coefficient of static friction, while the normal force is not, so long as the surface that's applying the normal force maintains it's structural integrity, therefore, the higher the angle of the banking, the faster you can go.

BTW, I've noticed you have posted lots of your circular motion problems looking for help. You should try and work them yourself and compare the answer to the book. If you got it wrong, it's important to your education to keep trying until you find out what you've done wrong. The explanation I've given for the two I've replied to is sufficient to answer all of these types of problems if you remember the part of centripetal force equaling the sum of the radial component of all forces, regardless of whether the forces are static friction forces (flat race track), normal forces (vertical banking, or ferris wheel), tension forces (swinging a string or a pendulum), or gravitational forces (orbit).

Remember Newton's first law. F=ma
If you want to accelerate a body, then forcenet should be applied.
And remember in a circular motion, the body is changing its direction where speed may be constant or changing, then the body is accelerating towards its center of the circle.

We have to supply this centripetal force. By string, gravity, friction or other means that supply the force.

Remember Newton's first law. F=ma
If you want to accelerate a body, then forcenet should be applied.
And remember in a circular motion, the body is changing its direction where speed may be constant or changing, then the body is accelerating towards its center of the circle.

We have to supply this centripetal force. By string, gravity, friction or other means that supply the force.
Thanks a lot. It did become an albatross. But I am slowly conquering my demons.