acceleration (toward the centre of the circle). This force is called CENTRIPETAL FORCE. Centripetal force can be supplie
Dynamics: Note 9
Uniform Circular Motion Centripetal Acceleration Uniform circular motion occurs when an object undergoes acceleration due to a change of direction, as opposed to a change of the magnitude of the velocity. An example is when a car travels around a traffic circle at constant speed. The direction of the object’s velocity is always tangential to the circle. The acceleration of an object is ALWAYS pointing toward the centre of the circle. To derive the formula for acceleration for uniform circular motion: • r1 = r2 because they are they are the radii of the same circle. Therefore, OPQ is an isosceles triangle. ! ! • v1 = v 2 because the speed is constant. • Each radius is perpendicular to its corresponding velocity • θ r = θ v since the angle between € corresponding members of sets of perpendicular lines are equal. This also makes these two triangles similar. € Derivation of Centripetal Acceleration Equation
Dynamics: Note 9 Centripetal Force Knowing Newton’s first law, an object will accelerate only if an external net force is acting on it. Because an object with uniform circular motion is always accelerating, there must be a net force acting on it. This force will act in the same direction as the acceleration (toward the centre of the circle). This force is called CENTRIPETAL FORCE. Centripetal force can be supplied by a number of different methods. For example, the moon is in a circular orbit around the earth due to gravity acting as a centripetal force. A car can stay on a circular on-ramp due to the friction between the tires and the road. A ball can travel in a circle at the end of a string, where the tension force in the string acts as a centripetal force. We can find the magnitude of this force using the following derivation: • Start with Newton’s second law: F = ma • Substitute in our formula for centripetal mv 2 F= acceleration in for the “a” term: r Comparison of Variables: As velocity increases, the force will _____________________ € As mass increases, the force will _____________________ As radius increases, the force will _____________________ Centrifugal Force This is a made up force. Imagine being on a merry-go-round while it is spinning. Which way do you want to move? You want to fly off the edge, away from the centre. But, centripetal force is a force toward the centre of the circle. Centrifugal force is a fictitious force to describe this phenomenon. What is actually happening in this case? Eg. 1. A 1500.0 kg car on a flat, horizontal road goes into a curve of constant radius. If the radius is 35.0 m, and the coefficient of static friction between the road and the tires is 0.50, what is the maximum speed that the car can have?
