lecture12 - Physic 231 Lecture 12 Main new points of todays...

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Physic 231 Lecture 12 Main new points of today’s lecture: Kinematic equations for circular motion: ( ) ( ) 0 0 t t 11 t 2 θω ωω α ω Δ= = + =+ Δ 00 222 22 1 t 2 2 θ + = + Δ Torque arm l ver the i Fd = eve e s d ; d τ
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Conceptual question An astronaut floating weightlessly in orbit shakes a large iron anvil rapidly back and forth. She reports back to Earth that – a) the shaking costs her no effort because the anvil has no inertial mass in space. – b) the shaking costs her some effort but considerably less than on Earth. – c) although weightless, the inertial mass of the anvil is the same as on Earth.
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Kepler’s laws Johannes Kepler proposed three laws of planetary motion: 1. All planets moved in elliptical orbits with the Sun at one of the focal points. 2a 2. Planetary orbits sweep out equal areas in equal times. (This is a consequence of angular momentum conservation.) r θ Δθ . const r t r 2 1 t t r 2 1 r r 2 1 area 2 2 2 = ω Δ ω Δ Δ θ Δ = θ Δ = 3. The square of the orbital period of any planet is proportional to the cube of the average distance from the planet to the Sun. For a circular orbit: 2 star planet planet rav planet c GM m m v Fm a == = 2 2 ω = = v GM star / / grav 2 rr 2 3 r r T T π 2 2 = = 2 3 2 = T r GM star 3 2 2 4 r GM T ar = 4. For an elliptical orbit: star 3 star 2 2 a GM 4 T π =
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Conceptual question Two satellites A and B of the same mass are going around Earth in concentric circular orbits.The distance of satellite B from Earth’s center is twice that of satellite A .What is the ratio of the entripetal force acting on that acting on centripetal force acting on B to that acting on A ? –a ) 1 / 8 –b ) 1 / 4 Es cc 2 GM m Fm a r == – c) 1/2 –d ) – e) 1 2 1 2 A 22 2 2 2 2 c,B BB B A B A 2 GM m r 11 F rr r r r r M 1 1 = = = 2 A c,A A B 2 2 AA A A GM m r F r r R B 2R A F c,B /F c,A ? 2 2 2 2 1 1/4 2 = Hint: This is a ratio problem.
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Example One satellite is in an orbit about Jupiter of radius r 1 and a period of 100 days. If a second satellite is placed in an orbit with 4 times the radius (i.e. r 2 =4r 1 ), what is the period for the orbit of the second satellite? –a ) 2 –b ) 4 –c ) 1 6 2 23 11 Jupiter 4 Tr GM π = –d ) 6 4 2 22 Jupiter 4 GM = r 2 4r 1 T 1 100 d 2 3 2 Jupiter 3 4 r GM 6 4 T 2 ? ( ) 2 3 1 Jupiter 46 4 r GM 2 21 1 T 8 T 8 T 8 100 days 800 days T
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Conceptual quiz Suppose Earth had no atmosphere and a ball were fired from the top of Mt. Everest in a direction tangent to the ground. If the initial speed were high enough to cause the ball to travel in a ircular trajectory around Earth the ball’s acceleration would
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lecture12 - Physic 231 Lecture 12 Main new points of todays...

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