Lecture 13 - PHYSICS 220 Lecture 13 Rotational Kinetic...

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PHYSICS 220 Lecture 13 Rotational Kinetic Energy and Inertia Lecture 13 Purdue University, Physics 220 1
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Rotations: Axes and Sign Lecture 13 Purdue University, Physics 220 2 When an object rotates, it has symmetry with respect to an axis . If the object is in the x-y axis a vector along the z-axis indicates the rotation direction The right-hand rule determines the direction of rotation Counter-clockwise is positive Clockwise is negative z + ω
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Rotational Kinetic Energy Lecture 13 Purdue University, Physics 220 3 A mass M on the end of a string is being spun around in a circle with radius r and angular velocity ω What is the object’s tangential velocity? M v = ω r Does the object have kinetic energy? K = 1 2 mv 2 K = 1 2 m ω r ( ) 2 K = 1 2 m ω 2 r 2
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Kinetic Energy of Rotating Disk Lecture 13 Purdue University, Physics 220 4 A disk with radius R and mass M is spinning with angular velocity ω r i Kinetic energy of one small piece of the wheel K i = 1 2 mv i 2 v i = ω r i K i = 1 2 mr i 2 ω 2 Sum all the individual pieces K Total = 1 2 mr i 2 ω 2 i Define I = mr i 2 i Moment of inertia K Total = I ω 2
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Rotational Moment of Inertia Lecture 13 Purdue University, Physics 220 5 Moment of inertia is a measure of how difficult it is to get an object rotating – It is the rotational analog of the inertia of Newton’s First Law The rotational moment of inertia depends on both the geometry of the object and the axis of rotation I = mr i 2 i kg m 2
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Rotational Inertia Table Lecture 13 Purdue University, Physics 220 6
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Symmetry in rotation and linear motion Lecture 7 Purdue University, Physics 220 7 ω = lim Δ t 0 Δ θ Δ t θ = θ 0 + ω t K = 1 2 I ω 2 v = lim Δ t 0 Δ x Δ t x = x 0 + vt K = 1 2 mv 2 p = m v v = ω r Connection between rotational and linear motion
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Rotational inertia example Lecture 13 Purdue University, Physics 220 8 Two batons have equal mass and length, which will be “easier” to spin about the center? 1. Mass on ends 2. Same 3. Mass in center
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Rotational inertia example Lecture 13 Purdue University, Physics 220 9 Two batons have equal mass and length, which will be “easier” to spin about the center? 1. Mass on ends 2. Same 3. Mass in center I = m i r i 2 i
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iClicker Question: Merry-Go-Round Lecture 13 Purdue University, Physics 220 10 B A Four kids, each having mass m, are riding on a (light) merry-go-round that rotates with an angular velocity ω = 3 rad/s .
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