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Unformatted text preview: PHYSICS 231 INTRODUCTORY PHYSICS I Lecture 11 • Angular velocity, acceleration • Rotational/ Linear analogy • (angle in radians) • Centripetal acceleration: (to center) Last Lecture " = #$ # t = $ f %$ i t f % t i ! = " f #" i t !" # ! x $ # v $ f # v f % # a t # t a t = r " v T = R " " s = r "# a cent = " 2 r = v 2 r " Newton’s Law of Universal Gravitation • Always attractive • Proportional to both masses • Inversely proportional to separation squared F = G m 1 m 2 r 2 G = 6.67 ! 10 " 11 m 3 kg # s 2 $ % & ’ ( ) Gravitation Constant • Determined experimentally • Henry Cavendish, 1798 • Light beam / mirror amplify motion Weight • Force of gravity on Earth • But we know F g = GM E m R E 2 F g = mg g = GM E R E 2 " Example 7.14 8.81 m/s 2 (0.90 g) Often people say astronauts feel weightless, because there is no gravity in space. This explanation is wrong! What is the acceleration due to gravity at the height of the space shuttle (~350 km above the earth surface)? Example 7.14 (continued) Correct explanation of weightlessness: • Everything (shuttle, people, bathroom scale, etc.) also falls with same acceleration • No counteracting force (earth’s surface) • “Accelerating Reference Frame” • Same effect would be felt in falling elevator Example 7.15a Astronaut Bob stands atop the highest mountain of planet Earth, which has radius R. Astronaut Ted whizzes around in a circular orbit at the same radius. Astronaut Carol whizzes around in a circular orbit of radius 3R. Astronaut Alice is simply falling straight downward and is at a radius R, but hasn’t hit the ground yet....
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 Spring '08
 smith
 Physics, Acceleration, General Relativity, Kepler's laws of planetary motion, Astronaut Alice

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