week4-2 - 1D-04 Radial Acceleration Tangential Velocity...

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1/31/2012 Physics 214 Fall 2010 1 1D-04 Radial Acceleration & Tangential Velocity AT ANY INSTANT, THE VELOCITY VECTOR OF THE BALL IS DIRECTED ALONG THE TANGENT. AT THE INSTANT WHEN THE BLADE CUTS THE STRING, THE BALL’S VELOCITY IS HORIZONTAL SO IT ACTS LIKE A HORIZONTALLY LAUNCHED PROJECTILE AND LANDS IN THE CATCH BOX. Once the string is cut, where is the ball going ? A). Continue with circular path B). Leave in a straight line C). Can not determine D). Leave like a horizontally launched projectile
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Discussion on Triangle, Arc and Cord θ α α θ α α θ α α θ α When θ is smaller, α is larger and the difference between the arc length and cord length are smaller. When θ is extremely small, α ≈90 o and the Length(arc) ≈ Length (cord) When θ is infinitely small, 0 o , α 90 o Length(arc) = Length (cord) Length (arc) =Length (cord) = r × r r r r
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Centripetal Acceleration a c v 2 r Imagining θ 0 ∆࢜ is perpendicular to v V is along the tangential direction of the circle v point to the center of the circle ∆࢜ = × ∆࢚ = ࢒ࢋ࢔ࢍ࢚ࢎ ( ࢇ࢘ࢉ ) = × = ∆࢜ ∆࢚ = θ θ α α α α r
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