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Rotation - Physics 201 Lecture 16 Rotational Kinematics...

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3/27/08 Physics 201, UW-Madison 1 Physics 201: Lecture 16 Physics 201: Lecture 16 Rotational Kinematics Analogy with one-dimensional kinematics Kinetic energy of a rotating system Moment of inertia Discrete particles Continuous solid objects
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3/27/08 Physics 201, UW-Madison 2 Question Question Consider the following situation: You are driving a car with constant speed around a horizontal circular flat track. On a piece of paper, draw a Free Body Diagram (FBD) for the car. Is the car being accelerated? A. Yes, radially inward B. Yes, radially outward C. No D. Insufficient information CORRECT
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3/27/08 Physics 201, UW-Madison 3 Rotational Variables... Rotational Variables... In Uniform Circular Motion ω was constant Now suppose ω can change as a function of time: We define the angular acceleration: θ ω α Consider the case when α is constant. Integrate ω and θ wrt time: Recall for a point a distance R from the axis of rotation: x = θ R Differentiating: v = ω R a = α R ! = d " dt = d 2 # dt 2 ! = ! 0 + " 0 t + 1 2 # t 2 ! = constant " = " 0 + ! t
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3/27/08 Physics 201, UW-Madison 4 Summary Summary (with comparison to 1-D kinematics) (with comparison to 1-D kinematics) Angular Linear And for a point at a distance R from the rotation axis: x = R θ v = ω R a = α R ! = constant ! = ! 0 + " t ! = ! 0 + " 0 t + 1 2 # t 2 ! = constant v = v 0 + at x = x 0 + v 0 t + 1 2 at 2
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3/27/08 Physics 201, UW-Madison 5 Question Question A ladybug sits at the outer edge of a merry-go-round that is turning and is slowing down. The vector expressing her angular velocity is A.
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