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Dynamics Of Circular Motion: Applications

### 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.

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