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When solving problems, you have found it useful to choose a coordinate system with one axis in the direction of the acceleration For circular motion, the direction of the acceleration is always toward the center of the circle Rather than labeling this axis x or y, call it c, for centripetal acceleration The other axis is in the direction of the velocity, tangent to the circle It is labeled tang for tangential You will apply Newton s second law in these directions, just as you did in the two-dimensional problems in 5 Remember that centripetal force is just another name for the net force in the centripetal direction It is the sum of all the real forces, those for which you can identify agents that act along the centripetal axis In the case of the hammer thrower in Figure 6-7, in what direction does the hammer fly when the chain is released Once the contact force of the chain is gone, there is no force accelerating the hammer toward the center of the circle, so the hammer flies off in the direction of its velocity, which is tangent to the circle Remember, if you cannot identify the agent of the force, then it does not exist

Uniform Circular Motion A 13-g rubber stopper is attached to a 093-m string The stopper is swung in a horizontal circle, making one revolution in 118 s Find the tension force exerted by the string on the stopper

Draw a free-body diagram for the swinging stopper Include the radius and the direction of motion Establish a coordinate system labeled tang and c The directions of a and FT are parallel to c Known:

Unknown:

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4 2r T2 4 2(093 m) (118 s)2

7:

118 s

26 m/s2 Use Newton s second law to find the tension in the string FT mac (0013 kg)(26 m/s2) Substitute m 0013 kg, ac 26 m/s2 034 N

Are the units correct Dimensional analysis verifies that a is in m/s2 and F is in N Do the signs make sense The signs should all be positive Are the magnitudes realistic The force is almost three times the weight of the stopper, and the acceleration is almost three times that of gravity, which is reasonable for such a light object

12 A runner moving at a speed of 88 m/s rounds a bend with a radius of 25 m What is the centripetal acceleration of the runner, and what agent exerts force on the runner 13 A car racing on a flat track travels at 22 m/s around a curve with a 56-m radius Find the car s centripetal acceleration What minimum coefficient of static friction between the tires and road is necessary for the car to round the curve without slipping 14 An airplane traveling at 201 m/s makes a turn What is the smallest radius of the circular path (in km) that the pilot can make and keep the centripetal acceleration under 50 m/s2 15 A 45-kg merry-go-round worker stands on the ride s platform 63 m from the center If her speed as she goes around the circle is 41 m/s, what is the force of friction necessary to keep her from falling off the platform

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