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# Lecture15_Pushkar - PHYSICS 220 Lecture 15 Angular Momentum...

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Lecture 15 Purdue University, Physics 220 1 Lecture 15 Angular Momentum PHYSICS 220

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Lecture 15 Purdue University, Physics 220 2 Linear vs Angular Linear Angular Displacement x θ Velocity v ϖ Acceleration a α Inertia m I KE ½ m v 2 ½ I ϖ 2 N2L F = ma τ = I α Momentum p = mv L = I ϖ
Lecture 15 Purdue University, Physics 220 3 Define Angular Momentum Momentum Angular Momentum p = mv L = I ϖ conserved if F ext = 0 conserved if τ ext = 0 Vector Vector units: kg*m/s units: kg*m 2 /s L = I ϖ = mr 2 v r = mvr = pr For a particle:

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Lecture 15 Purdue University, Physics 220 4 Right Hand Rule In general, for an object rotating about a fixed (z) axis we can write L z = I ϖ The direction of L z is + CCW, - CW Wrap fingers on right hand, around angle of rotation, thumb points in direction of L L z =I ϖ ϖ
Lecture 15 Purdue University, Physics 220 5 Spinning Disks A disk of mass M and radius R rotates around the z axis with angular velocity ϖ i . A second identical disk, initially not rotating, is dropped on top of the first. There is friction between the disks, and eventually they rotate together with angular velocity ϖ f . A) ϖ f = ϖ i B) ϖ f = ½ ϖ i C) ϖ f = ¼ ϖ i ϖ i z ϖ f z

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Lecture 15 Purdue University, Physics 220 6 First realize that there are no external torques acting on the two-disk system. Angular momentum will be conserved! ϖ 0 z 2 1 ϖ f z I ϖ i = 2 I ϖ f 1 2 ϖ i = ϖ f L i = I 1 ϖ 1 + 0 = I ϖ i L f = I 1 ϖ 1 + I 2 ϖ 2 = 2 I ϖ f
Lecture 15 Purdue University, Physics 220 7 Spin Up/Down

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Lecture15_Pushkar - PHYSICS 220 Lecture 15 Angular Momentum...

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