Lecture4 - Demo"Hitting a falling monkey You are a hunter...

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Demo: “Hitting a falling monkey” Solved in class tg θ = y Monkey0 x Monkey0 To hit the monkey we need to point the gun at it. You are a hunter and want to shoot a monkey on a tree at a distance x t0. In which direction should the projectile be fired? What should be v 0 ?
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A motion that repeat itself is called periodic motion . Example: The motion of a swinging ball. Periodic Circular motion |v 1 | |v 2 | |v 3 | |v 4 | |v 4 | |v 5 | |v 1 | = |v 2 | = …… |v n | BUT v changes continuously its direction a = 0 If the velocity is constant. What is the acceleration?
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|v 1 | |v 2 | |v 1 | |v 2 | a The acceleration points always toward the center Demo “Spinning Candles” No matter how fast it spins the acceleration points always to the center.
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|v 1 | |v 2 | (x, y) (r, θ ) More convenient coordinate system a x y R θ θ ANGULAR POSITION of the particle x y θ P 1 P 2 s r arc length θ = s r s = θ r θ needs to be measured in RADIANS Remember : 1 rad = 1 rad x 360 o / 2 π rad = 57.3 o 1 revolution = 360 o = 2 π rad Radial Coordinates
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Show Demo “Conical pendulum” What do we learn from this demo? Acceleration depends from the radius r increases a decreases Radial acceleration Δθ r 1 r 2 Δ s Δ s Δθ = r Δ v Δθ = r Δ s r = Δ v v Δ v v = Δ s r To find acceleration divide by Δ t: Δ v v = Δ s r Δ t Δ t a = v 2 r = a RADIAL DEF RADIAL or CENTRIPETAL ACCELERATION Equivalent to v 2 Δθ v 1 Δ v
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Angular Velocity and Period Δθ r 1 r 2 Δ s ω = d θ d t Δ θ Δ t lim Δθ 0 = Definition [ ω ] = [rad] / [sec]
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This note was uploaded on 04/03/2008 for the course PHYSICS 7A taught by Professor Lanzara during the Spring '08 term at Berkeley.

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Lecture4 - Demo"Hitting a falling monkey You are a hunter...

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