6 - Circular Motion and Other Applications of Newton's Laws

62 when the string breaks the ball moves in the

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Unformatted text preview: all moves in the direction tangent to the circle. r A force causing a centripetal acceleration acts toward the center of the circular path and causes a change in the direction of the velocity vector. If that force should vanish, the object would no longer move in its circular path; instead, it would move along a straight-line path tangent to the circle. This idea is illustrated in Figure 6.2 for the ball whirling at the end of a string. If the string breaks at some instant, the ball moves along the straight-line path tangent to the circle at the point where the string broke. Quick Quiz 6.1 Is it possible for a car to move in a circular path in such a way that it has a tangential acceleration but no centripetal acceleration? CONCEPTUAL EXAMPLE 6.1 An athlete in the process of throwing the hammer at the 1996 Olympic Games in Atlanta, Georgia. The force exerted by the chain is the force causing the circular motion. Only when the athlete releases the hammer will it move along a straight-line path tangent to the circle. Forces That Cause Centripetal Acceleration The force causing centripetal acceleration is sometimes called a centripetal force. We are familiar with a variety of forces in nature — friction, gravity, normal forces, tension, and so forth. Should we add centripetal force to this list? Solution No; centripetal force should not be added to this list. This is a pitfall for many students. Giving the force causing circular motion a name — centripetal force — leads many students to consider it a new kind of force rather than a new role for force. A common mistake in force diagrams is to draw all the usual forces and then to add another vector for the centripetal force. But it is not a separate force — it is simply one of our familiar forces acting in the role of a force that causes a circular motion. Consider some examples. For the motion of the Earth around the Sun, the centripetal force is gravity. For an object sitting on a rotating turntable, the centripetal force is friction. For a rock whirled on the end of a string, the centripetal force is the force of tension in the string. For an amusementpark patron pressed against the inner wall of a rapidly rotating circular room, the centripetal force is the normal force exerted by the wall. What’s more, the centripetal force could be a combination of two or more forces. For example, as a Ferris-wheel rider passes through the lowest point, the centripetal force on her is the difference between the normal force exerted by the seat and her weight. 154 CHAPTER 6 Circular Motion and Other Applications of Newton’s Laws (a) (b) (c) (d) Figure 6.3 A ball that had been moving in a circular path is acted on by various external forces that change its path. Quick Quiz 6.2 QuickLab Tie a string to a tennis ball, swing it in a circle, and then, while it is swinging, let go of the string to verify your answer to the last part of Quick Quiz 6.2. A ball is following the dotted circular path shown in Figu...
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