5.1

Uniform Circular Motion

There are many examples of motion on a circular path. Of the many possibilities, we single out those that satisfy the following definition:

| Definition of Uniform Circular Motion
| Uniform circular motion is the motion of an object traveling at a constant (uniform) speed on a circular path.

As an example of uniform circular motion, Figure 5-1 shows a model airplane on a guideline. The speed of the plane is the magnitude of the velocity vector , and since the speed is constant, the vectors in the drawing have the same magnitude at all points on the circle.

Figure 5-1 The motion of a model airplane flying at a constant speed on a horizontal circular path is an example of uniform circular motion.

Sometimes it is more convenient to describe uniform circular motion by specifying the period of the motion, rather than the speed. The period T is the time required to travel once around the circle—that is, to make one complete revolution. There is a relationship between period and speed, since speed v is the distance traveled () divided by the time T:

| (5.1)

If the radius is known, as in Example 1, the speed can be calculated from the period, or vice versa.

| Example 1 | | | A Tire-Balancing Machine

The wheel of a car has a radius of r = 0.29 m and is being rotated at 830 revolutions per minute (rpm) on a tire-balancing machine. Determine the speed (in m/s) at which the outer edge of the wheel is moving. Reasoning The speed v can be obtained directly from , but first the period T is needed. The period is the time for one revolution, and it must be expressed in seconds, because the problem asks for the speed in meters per second.
Solution Since the tire makes 830 revolutions in one minute, the number of minutes required for a single revolution is

Therefore, the period is , which corresponds to 0.072 s. Equation 5.1 can now be used to find the speed:

The definition of uniform circular motion emphasizes that the speed, or the magnitude of the velocity vector, is constant. It is equally significant that the direction of the vector is not constant. In Figure 5-1, for instance, the velocity vector changes direction as the plane moves around the circle. Any change in the velocity vector, even if it is only a change in direction, means that an acceleration is occurring. This particular acceleration is called “centripetal acceleration,” because it points toward the center of the circle, as the next section explains.

Copyright © 2007 John Wiley & Sons, Inc. All rights reserved.