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Unformatted text preview: March 19, 2006 Physics for Scientists&Engineers 1 1 Physics for Scientists & Physics for Scientists & Engineers 1 Engineers 1 Spring Semester 2006 Lecture 31 March 19, 2006 Physics for Scientists&Engineers 1 2 Review: Angular Velocity Review: Angular Velocity ! Angular velocity: Average: Instantaneous: ! Frequency: ! Period: ! = " 2 # " 1 t 2 # t 1 = $ " $ t ! = lim " t # ! = d $ dt f = ! 2 " # ! = 2 " f T = 1 f March 19, 2006 Physics for Scientists&Engineers 1 3 Review: Linear and Angular Velocity Review: Linear and Angular Velocity ! Linear velocity vector points in tangential direction ! Magnitude: r v = r ! t v = r ! March 19, 2006 Physics for Scientists&Engineers 1 4 Example: Earth Example: Earth ! Question: The Earth orbits around the Sun and revolves around its own pole-to-pole axis. What are the corresponding angular velocities, frequencies, and linear speeds? ! Answer: Any point on the surface of Earth moves in circular motion around the rotation axis (pole-to-pole) axis, with a rotation period of 1 day. Expressed in seconds, this period is ! The Earth moves around the Sun on an elliptical path, which is very close to circular. The orbital period for the motion of the Earth around the Sun is 1 year. If we express this period in seconds, we obtain: T earth = 1 day ! 24 hour day ! 3600 s hour = 8.64 ! 10 4 s T sun = 1 year ! 365 day year ! 24 hour day ! 3600 s hour = 3.15 ! 10 7 s March 19, 2006 Physics for Scientists&Engineers 1 5 Example: Earth (2) Example: Earth (2) ! Both circular motions have constant angular velocity. Thus, we can use T =1/ f and ! =2 " f to obtain our answers: f...
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