Lecture 13

# 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
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
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
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
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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