Chapter 6 - Chapter 6 Circular Motion and Gravitation We...

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1 Chapter 6: Circular Motion and Gravitation We briefly discussed motion at constant speed in a circle. Now that we know about forces, we can look again at this. We’ll also introduce Newton’s theory of gravitation which often causes circular motion. Uniform Circular Motion - a reminder An object moving at constant speed around a circular path has an acceleration pointing radially inward no acceleration component parallel to the velocity? - that would change the speed! we found a formula Uniform Circular Motion - dynamics So what happens if we remove the force? e.g. what if the string is cut? vote: 1. particle stops where it is 2. particle moves at constant speed along the radial direction 3. particle moves at constant speed in the tangential direction Example 6.1 Model airplane on a string Fly a propeller-driven model airplane on a 5.00m string in a horizontal circle. The airplane, which has mass 0.500kg flies level and at constant speed and makes one revolution every 4.00 seconds. How hard must you pull on the string to keep the plane flying in a circle? radial acceleration speed
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2 Example 6.4 Rounding a banked curve An engineer wants to bank a curve so that, at a certain speed, v , no friction is needed for a car to take the curve. At what angle should it be banked if v = 25 m/s (56 mph)? vertically - no acceleration we’re using the horizontal component of the normal force to cause the radial acceleration Example 6.5 Dynamics of a Ferris wheel ride A passenger of mass m , riding on a Ferris wheel moves in a vertical circle of radius R with constant speed v . (a) assuming that the seat remains upright during the motion, derive expressions for the magnitude of the upward force the seat exerts on the passenger at the top and bottom of the circle (b) What are these forces if m = 60.0 kg, the radius of the circle is R = 8.00 m and the wheel makes on revolution in 10.0 s? How to they compare to the passenger’s actual weight?
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Chapter 6 - Chapter 6 Circular Motion and Gravitation We...

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