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ps1slns - Physics 8.01 Assignment 1 1.1 Figure 1 sunset We...

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Physics 8.01 Assignment 1 1.1 Figure 1: sunset We treat the sun as an object that is rotating about the earth with uniform angular velocity, and that rises and sets vertically (this is assured by being on the equator on the equinox). We first need to know the angle sun must rotate through during the sunset ( α ). If we can then get the angular speed of the sun as we see it we can get the time it takes for the sunset. α is small α tan α = D R 1
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D = 13 . 92 × 10 8 m R = 1 . 50 × 10 11 m α = 9 . 28 × 10 3 radians The angular velocity follows from fact sun will rotate 2 π radians during 24 hours: ω sun = 2 π 24 × 60 × 60 = 7 . 27 × 10 5 radians s The time is the angular size of the sun divided by the angular velocity, analogous to the case with distance and linear velocity. T sunset = α ω sun = 9 . 28 × 10 3 7 . 27 × 10 5 = 128 s 2 min. 2
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1.2 a) Dimensional consistency of v : m s x : m a : m s 2 RHS: m 2 s 2 LHS: m 2 s 2 + m × m s 2 m 2 s 2 b) Both LHS and RHS have the same dimensions. These are now multiplied by mass with units kg .
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