![]() ![]() ![]() The acceleration of the object is dependent upon this velocity change and is in the same direction as this velocity change. At the midpoint along the arc connecting points A and B, the velocity change is directed towards point C - the center of the circle. A careful inspection of the velocity change vector in the above diagram shows that it points down and to the left. Note in the diagram above that there is a velocity change for an object moving in a circle with a constant speed. The process of subtracting v i from v f is shown in the vector diagram this process yields the change in velocity. In this time, the velocity has changed from v i to v f. In a time of t seconds, the object has moved from point A to point B. Consider the case of an object moving in a circle about point C as shown in the diagram below. ![]() But the addition and subtraction of vectors from each other is done in a manner much different than the addition and subtraction of scalar quantities. The numerator of the equation is found by subtracting one vector ( v i) from a second vector ( v f). Where v i represents the initial velocity and v f represents the final velocity after some time of t. ![]() As such, it is calculated using the following equation: Recall from Unit 1 of The Physics Classroom that acceleration as a quantity was defined as the rate at which the velocity of an object changes. To understand this at a deeper level, we will have to combine the definition of acceleration with a review of some basic vector principles. It is accelerating because the direction of the velocity vector is changing. For this reason, it can be safely concluded that an object moving in a circle at constant speed is indeed accelerating. And since velocity is a vector that has both magnitude and direction, a change in either the magnitude or the direction constitutes a change in the velocity. But the fact is that an accelerating object is an object that is changing its velocity. "After all," they might say, "if I were driving a car in a circle at a constant speed of 20 mi/hr, then the speed is neither decreasing nor increasing therefore there must not be an acceleration." At the center of this common student misconception is the wrong belief that acceleration has to do with speed and not with velocity. Because the speed is constant for such a motion, many students have the misconception that there is no acceleration. The velocity vector is constant in magnitude but changing in direction. As mentioned earlier in Lesson 1, an object moving in uniform circular motion is moving in a circle with a uniform or constant speed. ![]()
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