When an object moves in a curved path, like a race car on a banked track or a bicycle turning a corner, banked curves and horizontal circular motion come into play. In these situations, the angle of banking plays a crucial role in allowing the object to move safely and efficiently. Banked curves are designed such that the track is slightly tilted towards the center of the curve. This tilt helps counteract the centrifugal force and ensures that the object remains on the intended path. If the curve is not banked, friction between the object's tires or wheels and the surface is relied upon to prevent sliding outwards. However, this poses a limit on the maximum speed at which the object can safely travel around the curve.

Banking angle is determined by various factors such as speed, radius of curvature, and the coefficient of friction between the tires and the road surface. The ideal angle of banking can be calculated using the formula: θ = tan⁻¹(v² / (g × r)), where θ is the banking angle, v is the speed of the object, g is the acceleration due to gravity, and r is the radius of the curve. By adjusting the angle of banking, engineers can ensure that the object moves smoothly around the curve without the need for excessive friction or relying solely on the tires' grip.

Another concept related to circular motion is horizontal circular motion. In this scenario, the object moves in a horizontal circle while remaining parallel to the ground. A simple example of horizontal circular motion is swinging a yo-yo in a circle. In this case, the string exerts a force, known as the tension force, on the yo-yo, keeping it in circular motion.

In horizontal circular motion, the net force exerted on the object is zero in the horizontal direction. This means that the centripetal force required to keep the object moving in a circle must be provided by a different force. For instance, in the case of a yo-yo, tension in the string acts as the centripetal force. Velocity is always tangent to the circular path, while acceleration is directed towards the center of the circle. It's important to note that in horizontal circular motion, the speed remains constant, but the direction of velocity constantly changes. So, while the object does not accelerate in terms of magnitude, it experiences centripetal acceleration towards the center of the circular path.