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Unformatted text preview: 1 Lecture 16 2200 ϖ and α as vectors • Rotational kinetic energy • Moment of inertia • Parallel axis theorem It will be a good idea to review lecture 9. 2 Linear and angular motion Independent variable Timet Timet Variable coordinate Positionx Angle θ First derivative Velocity Angular velocity Second derivative Acceleration Angular acceleration Constant acceleration formulas Where Where dt dx v = dt d θ ϖ = 2 2 dt x d a = 2 2 dt d θ α = x a v v at t v x x at v v ∆ + = + + = + = 2 2 1 2 2 2 θ α ϖ ϖ α ϖ θ θ α ϖ ϖ ∆ + = + + = + = 2 2 1 2 2 2 t t t ( 29 ( 29 = = = = t v v t x x ( 29 ( 29 = = = = t t ϖ ϖ θ θ 3 What is the direction of ϖ ? Use a right hand rule: curl the fingers of your right hand in the direction of rotation and your thumb will point in the direction of ϖ . Your thumb defines the rotation axis. z ( 29 z ω ˆ + = ϖ 4 The period of the rotation is the time it takes to complete one cycle. T t π θ ϖ 2 ave = ∆ ∆ = For 1 cycle. T is the period. ϖ π 2 = T 5 Kinetic energy of rotation In a discrete or continuous distribution of mass each mass point has K=½mv 2 . So ∑ = = + + + = n i i i n n v m v m v m v m K 1 2 2 2 2 2 2 1 1 rot 2 1 2 1 2 1 2 1 For a rotating rigid body v i = ϖ r i where r i is the distance from the rotation axis to the mass m i ....
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 Spring '11
 Staff
 Angular Momentum, Energy, Inertia, Kinetic Energy, Moment Of Inertia, Rotation, Angular Acceleration, Ri

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