# DQ1D_solution - ω of the motion and the radius R of the...

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Discussion Question 1D P212, Week 1 P211 Review: Uniform Circular Motion page 1 2 1 ˆ r 12 r 12 , F 1 2 =− G m 1 m 2 r 12 2 ˆ r 12 In P112 you will encounter problems where charged particles move in uniform circular motion. The forces involved may be electric or magnetic in nature. The answer to part(e) contains the secret of the cyclotron. Kepler’s Third Law (K-III) for planetary motion about the sun for circular orbits is T 2 = CR 3 where T is the period, R is the radius of the planet’s orbit and C is a constant. (a) Derive K-III for a circular orbit and in the process find an algebraic expression for C in terms the mass of the sun M S , the universal gravitational constant G , and numerical factors. F = -G m M S / R 2 F = ma = -m v 2 / R Set equal to each other and substitute period for velocity. T 2 = 4 π 2 R 3 / (G M S ) (b) Using your answer from part (b), re-express K-III as a relationship between the angular frequency

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