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**Unformatted text preview: **Chapter 11: Rolling, Torque, and Angular Momentum
111 What Is Physics? 112 Rolling as Translation and Rotation Combined 113 The Kinetic Energy of Rolling 114 The Forces of Rolling 115 The YoYo 116 Torque Revisited 117 Angular Momentum 118 Newton's Second Law in Angular Form 119 The Angular Momentum of a System of Particles 1110 The Angular Momentum of a Rigid Body Rotating ... 1111 Conservation of Angular Momentum 1112 Precession of a Gyroscope Chapter 11 Homework 2, 4, 5, 7, 11, 17, 23, 27, 31, 34, 36, 41, 43, 45, 52, 58 Examples
Homework Problem 23. Find torque, and the angle b/t F and r. ^ + (4.0 m)^ , F = (-8.0 N)^ + (6.0 N)^ r = (3.0 m)i j i j Sample Problem 11-4. Find the net angular momentum about O. =rp = r p 5.0 kgm/s 2.0 m 4.0 m 2.0 kgm/s Newton's 2nd Law net net,ext = Lsys = Linear Motion dp Fnet = dt d = dt dLsys dt Fnet,ext = Psys = dPsys dt pi 2 i 2 Rigid body, fixed axis (z) Lz = I
L2 K = I = 2I
1 2 Psys = Mvcom
p2 K = mv = 2m
1 2 Examples
Sample Problem 11-5. Find the angular momentum and torque about O at time t. Sample Problem 11-6. Ferris Wheel avg L = t Conservation of
Angular Momentum net,ext = dLsys dt Linear Motion Conservation Law for Closed, Isolated systems Psys = constant Lsys = constant If the net external torque on a system is zero, the angular momentum of the system remains constant. If the component of the net external torque on a system along a certain axis is zero, then the component of the angular momentum of the system along that axis cannot change. Lz = constant if z = 0 Examples
Changing Moment of Inertia L z = I ii = I f f
Sample Problem 11-8. r = 0.800R, M = 6m = 1.50 rad/s Examples
Sample Problem 11-7. Example. Collision Precession of a Gyroscope
Youtube Video dL = dt L (t + dt ) = L (t ) + dt ...

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