6.8:
Dynamics Of Circular Motion: Applications
When a car is moving in a circular path at a constant speed, the forces acting are the static frictional force, its weight, and the normal force.
In the horizontal direction, the radial static frictional force provides the necessary centripetal force for the circular motion and is the product of friction coefficient and normal force.
In the vertical direction, normal force equals the car's weight.
By substituting for N and solving for velocity, the maximum speed of the car can be obtained.
Beyond this speed, the static friction reduces and the vehicle will skid outwards.
Hence, racing tracks designed for high-speed travel have banked curves. The road slope with a greater banking angle helps the vehicle travel at higher speeds without relying on friction.
On a banked road, the horizontal normal force component acting towards the center of the curve provides the centripetal force, while the vertical normal force component balances the car's weight.
Dividing the two equations, an expression for the required banking angle and the car's maximum speed is obtained.
6.8:
Dynamics Of Circular Motion: Applications
Suppose a car moves on flat ground and turns to the left. The centripetal force causing the car to turn in a circular path is due to friction between the tires and the road. For this, a minimum coefficient of friction is needed, or the car will move in a larger-radius curve and leave the roadway. Let's now consider banked curves, where the slope of the road helps in negotiating the curve. The greater the angle of the curve, the faster one can take the curve. It is common for race tracks for bikes and cars to have steeply banked curves. In an "ideally banked curve," the angle is such that one can negotiate the curve at a certain speed without the aid of friction between the tires and the road. For ideal banking, the net external force equals the horizontal centripetal force in the absence of friction. Also, the components of normal force in the horizontal and vertical directions must equal the centripetal force and the weight of the car, respectively.
As an example, we can also examine airplanes that also turn by banking. The lift force from the force of the air on the wing acts at right angles to the wing. When the airplane banks, the pilot is obtaining greater lift than necessary for level flight. The vertical component of lift balances the airplane's weight, and the horizontal component accelerates the plane.
This text is adapted from Openstax, University Physics Volume 1, Section 6.3: Centripetal Force.