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2c_lec4 - Physics 2A Olga Dudko UCSD Physics Lecture 4...

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Today: Principle of Galilean relativity. Projectile motion. Circular motion. Physics 2A Olga Dudko UCSD Physics Lecture 4
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Relative Motion: the book notations
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Principle of Galilean relativity Galileo Galilei first described this principle in 1632 in his Dialogue Concerning the Two Chief World Systems =>
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Independence of vertical and horizontal motions • The kinematics equations that we derived for 1D motion (with a = const) hold in 2D. • But the equations apply separately to each component of 2D motion. • BIG PHYSICS CONCEPT: Perpendicular components of motion are independent of each other. => Giving an object velocity or acceleration in the horizontal direction does not affect how fast it falls to the ground. drop shoot
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Kinematics Equations in 2D => for motion in 2D the individual components of motion obey the following equations as long as a x and a y are constants: v y 2 = v 0 y 2 + 2 a y Δ y Δ y = v 0 y t + 1 2 a y t 2 Δ y = 1 2 ( v 0 y + v y ) t v y = v 0 y + a y t v x 2 = v 0 x 2 + 2 a x Δ x Δ x = v 0 x t + 1 2 a x t 2 Δ x = 1 2 ( v 0 x + v x ) t v x = v 0 x + a x t Note: subscripts now denote variables that are in the x and y directions (except for t - the link btw the two sets of equations).
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We will neglect air resistance. Krakatau volcano eruption, Indonesia. Nat.Geographic Projectile Motion
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Typical projectile motion problem y x
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Projectile Motion θ v 0 y v 0 y x v 0 y = ϐഏ v 0 ϐഏ sin θ v 0 y = (100 m/s) sin30º = (100 m/s) =50.0 m/s 1 2 v 0 x = ϐഏ v 0 ϐഏ cos θ v 0 x = (100 m/s) cos30º = (100 m/s) =86.6 m/s 3 2 v 0 x • Use the kinematics equations separately in each direction.
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Projectile Motion • Let’s try the x-direction. List the quantities we know: v ox = +86.6m/s a x = Don’t know: • 3rd eq.: • Other eqs.? Δ x = v 0 x t + 1 2 a x t 2 Δ x = v 0 x t 0 v x , t, Δ x (finding) v x 2 = v 0 x 2 + 2 a x Δ x Δ x = v 0 x t + 1 2 a x t 2 Δ x = 1 2 ( v 0 x + v x ) t v x = v 0 x + a x t 0 m/s 2 = constant => v x 2 = v 0 x 2 + 2 a x Δ x Δ x = 1 2 ( v 0 x + v x ) t v x = v 0 x + a x t Δ x = v 0 x
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