Students will learn that in circular motion there is always an acceleration (and hence a force) that points to the center of the circle defined by the objects motion. This force changes the direction of the velocity vector of the object but not the speed. Students will also learn how to calculate that speed using the period of motion and the distance of its path (circumference of the circle it traces out).
centripetal acceleration: The inward acceleration that keeps an object in circular motion.
centripetal force: The inward force that keeps an object in circular motion.
A satellite orbits around the Earth in Figure below. A car travels around a curve in Figure below. All of these objects are engaged in circular motion. Let us consider the satellite first. The satellite is held in place by the Earth’s gravity. The gravity holds the satellite in its orbit. In what direction does this force act? If the earth were “magically” gone, the satellite would fly off tangent to its motion at the instant gravity no longer held it. The force preventing this from happening must keep pulling the satellite toward the center of the circle to maintain circular motion.
Figure below shows the instantaneous velocity vectors for the car in two different positions a very small time apart.
Illustrative Examples using Centripetal Acceleration and Force
Example 1A: A 1000 kg car moves with a constant speed 13.0 m/s around a flat circular track of radius 40.0 m. What is the magnitude and direction of the centripetal acceleration?
Example 1b: Determine the force of static friction that acts upon the car in Figure below.
Example 1c: Determine the minimum necessary coefficient of static friction between the tires and the road.
Check Your Understanding
True or False?
1. Kinetic friction is responsible for the traction (friction) between the tires and the road.
Answer: False. As long as the car does not skid, there is no relative motion between the instantaneous contact area of the tire and the road.
2. True or False? The force of static friction upon an object can vary.
3. The greater the mass of the car, the greater the coefficient of friction.
Answer: False. The coefficient of friction is independent of the mass of an object. Recall that it is the ratio of the friction force to the normal force. As such, it is a pure number dependent only upon the nature of the materials in contact with each other- in this case rubber and asphalt.