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Unformatted text preview: Translational vs Rotational Motion Rotational speed = 2/T Translational speed v = 2r/T v = r Rotational speed = d/dt Translational speed v = ds/dt d ds For one complete rotation Angular and Rotational are used interchangeably. Angular acceleration = d/dt a =r Rolling Wheel Direction of Translational vs Rotational Motion (cont) In rotational motion force is replaced by torque, . In rotational motion inertia is measured as moment of inertia, I . In translational motion inertia is measured by mass, m. Moment of inertia, I , depends on the amount and location of mass. = r x F Newtons Second Law (rotational motion) = I Rotational (Angular) Momentum L = I The greater the distance the mass is from the center of rotation. the greater the Moment of inertia. I Disk = mr 2 I Ring = mr 2 Rotational Kinetic Energy. K R = I 2 Translational vs Rotational Motion (cont) Moments of Inertia Disk vs Ring E A = E B U A = K B (mgh) = mv 2 + I 2 v h A B (mgh) = mv D 2 + ( mr 2 ) (v D /r) 2 gh = v D 2 + v D 2 (4 gh/3) 1/2 = v D For a disk I = mr 2 For a ring I = mr 2 (mgh) = mv R 2 + (mr 2 )(v R /r) 2 gh = v R 2 + v R 2 gh = v R 2 (gh) 1/2 = v R v D /v R = (4/3) 1/2 v D /v R = 1.15 v D = 1.15v R Since neither m nor r are factors Any Disk will beat any Ring !...
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 Spring '08
 Dr.Schrieber
 Physics, Angular Momentum, Moment Of Inertia, Rigid Body, Rotation

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