10_1425_web_Lec_09_CircularMotion

10_1425_web_Lec_09_CircularMotion - Circular Motion Physics...

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Circular Motion Physics 1425 Lecture 9 Michael Fowler, UVa.
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A Cannon on a Mountain Back to Galileo one more time… imagine a powerful cannon shooting horizontally from a high mountaintop: The path falls 5 m below a horizontal line in one second.
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Newton’s Idea: a Really High Mountain Imagine a very powerful cannon atop a mountain beyond the Earth’s atmosphere. This cannonball goes so far we have to include the Earth’s curvature in our calculations! The Earth’s surface drops 5m below a horizontal plane on traveling 8 km. So what happens if the cannonball goes at 8 km/sec?
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After Traveling 8 Kilometers in 1 second… The cannonball’s velocity has slightly changed direction, adding about g = 10 m/sec downwards , so the angle of change is given by tan θ =10/8000. BUT the Earth’s surface underneath the cannonball has turned by precisely the same amount—and so has the direction of gravity! The cannonball finds itself in exactly the same situation it began in : moving parallel to the surface, perpendicular to gravity, at the same height. So what happens next?
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Newton’s Own Picture Newton realized that at the right initial speed, above the atmosphere, the cannonball would circle indefinitely, accelerating towards the Earth constantly, but staying at the same height .
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10_1425_web_Lec_09_CircularMotion - Circular Motion Physics...

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