Ideal banking

Definition

Ideal banking is the design of a curve on a road or track where the angle of the bank allows vehicles to navigate the turn without relying on friction. The banked angle provides the necessary centripetal force to keep the vehicle moving in a circular path.

5 Must Know Facts For Your Next Test

1. In ideal banking, the frictional force is zero or minimized.
2. The optimal banking angle depends on the speed of the vehicle and the radius of the curve.
3. The formula for calculating ideal banking angle is $\tan(\theta) = \frac{v^2}{rg}$, where $\theta$ is the banking angle, $v$ is velocity, $r$ is radius, and $g$ is gravitational acceleration.
4. Ideal banking reduces wear and tear on tires since less reliance is placed on friction.
5. Real-world applications include highway exit ramps and race tracks.

Review Questions

• What conditions must be met for a curve to be considered ideally banked?
• How does an increase in vehicle speed affect the ideal banking angle?
• Derive the formula for calculating ideal banking angle using centripetal force concepts.

Related terms

Centripetal Force: The inward force required to keep an object moving in a circular path at constant speed.

Friction: The resistive force that occurs when two surfaces move across one another. It acts tangentially to surfaces in contact.

Radius of Curvature: The distance from the center of a circle to any point on its perimeter. In curved paths, it determines how sharp or gentle a turn is.