alittlebitofcalculus-pdf-january2011-111112001007-phpapp01

T is time exer ercise ex er cise 7 with the bouncing

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Unformatted text preview: an axis or point then the elements of mass of the rigid body, regardless of the distance from the axis or elements point of rotation, have the same angular velocity. If the angular velocity is ω then : / kinetic energy of rotation = 1 2Iω2 . / This is analogous to the kinetic energy of linear motion = 1 2mv 2 . 196 IY = ∫ dIY = 197 IY = MR2 2π 2π 0 0 ∫ M/ R2dθ = MR2/ . [θ ] 2π 2π The moment of iner tia of the entire ring about the central y-axis is : moment inertia 2 dIY = M/2πR . (Rdθ ) . R2 = MR /2π . dθ d The moment of iner tia of this element about the central y-axis is: moment inertia element d The mass of an element (= d arc) of the ring is: dM = M/2πR . (Rdθ ) . element Since the mass is of uniform density we have: mass per unit length = M/2πR . The circumference of the ring is 2πR. x 0987654321098765432121098765432109876543210987654321 0987654321098765432121098765432109876543210987654321 0987654321098765432121098765432109876543210987654321 0987654321098765432121098765432109876543210987654321 0987654321098765432121098765432109876543210987654321 0987654321098765432121098765432109876543210987654321 0987654321098765432121098765432109876543210987654321 098765432109876...
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This note was uploaded on 11/29/2012 for the course PHYSICS 105 taught by Professor Tamerdoğan during the Fall '09 term at Middle East Technical University.

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