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# ps04sol - 8.01T Problem Set 4 Solutions Fall 2004 Problem 1...

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8.01T Problem Set 4 Solutions Fall 2004 Problem 1. Rotational Kinematics. a) In 2004, the period of rotation is T E = 86164 s . Thus the angular velocity is 2 1 θ E = 7 10 5 s T E The radius of the circle of rotation of the person at MIT is r = R E cos 4 . 71 10 6 m. Hence the linear velocity is 2 v = θ E r = R E cos 343 . 7 m/s T E and the centripetal acceleration is a = θ 2 r 0 . 025 m/s 2 . E b) The average angular deceleration is E θ E 2 2 = = ( T 2004 T 1924 ) T 2 ( T 2004 T 1924 ) dt t T 2004 T 1924 t 2004 t where T 2004 and T 1924 refer to the period of the Earth’s rotation in 2004 in 1924 and t = 80 years. Substituting numbers, we obtain E 2 9 10 22 s dt Problem 2. Second Law Applications. a) The force diagram is shown on Fig. 1. b) Using the coordinate system shown on Fig. 1, we get r : T 1 sin + T 2 sin = ma r = 2 l sin y : T 1 cos T 2 cos mg = 0 , 1

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± ± 8.01T Problem Set 4 Solutions Fall 2004 F total T mg 1 y r T 2 Figure 1: Force diagram for
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ps04sol - 8.01T Problem Set 4 Solutions Fall 2004 Problem 1...

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