# HW 5 - Problem 4.28 The radius of the earths nearly...

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Problem 4.28: The radius of the earth’s nearly circular orbit around the sun is 1.5 X 10 11 m. Find the magnitude of the earth’s a) velocity, b) angular velocity and c) centripetal acceleration as it travels around the sun. Assume a year of 365 days. Knowns: r=1.5 X10 11 m T=365 days Find: V,w,a A] v= 2 ʋ r T =2 ʋ X1.5 X 10 11 m 1day 1hr . 1min 365 days 24hr 60min 60 s =3 X 10 4 m/s B] w= v = 3.0X10 4 m/s r 1.5 X 10 11 m =2.0 X 10 -7 rad/s

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C] a= v 2 = (3 X 10 4 ) 2 r 1.5 X 10 11 = 6.0 X 10 -3 ms -2 Problem 4.35: A 5.0 m diameter merry-go-round is initially turning with a 4.0 s period. It slows down and stops in 20s. A]Before slowing, what is the speed of a child on the rim? B] How many revolutions does the merry-go-round make as it stops. Knowns: r= 2.5 m T= 4.0 s ѐ t=20s W f =0 rad/s Finds: V i , ̩ A] v i = Ϯʋ r =2 ʋ X2.5m = 3.93 m/s T 4s B] w i = v i = 3.93m/s r 2.5m
=1.57 rad/s W f = w i нɲѐ t Or ɲ =-1.57rad/s =-0.08 rad/s 2 20s Then, W f 2 = w i 2 +2 ɲѐ̩ Or, ѐ̩ =15.41 rad

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HW 5 - Problem 4.28 The radius of the earths nearly...

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