1. Chapter 11 Angular Momentum; General Rotation 11-2 Vector Cross Product; Torque as a Vector 11-3Angular Momentum of a Particle 11-4 Angular Momentum and Torque for a System of Particles; General Motion 11-5 Angular Momentum and Torque for a Rigid Object 11-6 Conservation of Angular Momentum 14-1 Simple Harmonic Motion HW#9:Chap.11:Pb.11, Pb.21, Pb.24, Pb.32,Pb.41, Pb.51 Due Wednesday, Dec. 3 after Thanksgiving break

2.  orque  orque  orque  orque  orque  orque  orque  orque  orque Motion of Rolling Objects For the solid ball For the hollow ball Rolling objects have rotational and translational Kinetic Energy

3.  orque  orque  orque  orque  orque  orque  orque  orque  orque Questiom You are skating and you spin with your arms outstretched. When you bring your arms in close to your body, your moment of inertia A) increases B) decreases C) stays the same

4.  orque  orque  orque  orque  orque  orque  orque  orque  orque Questiom You are skating and you spin with your arms outstretched. When you bring your arms in close to your body, your angular velocity A) increases B) decreases C) stays the same

5.  orque  orque  orque  orque  orque  orque  orque  orque  orque 11-2 Vector Cross Product; Torque as a Vector The vector cross product is defined as: The direction of the cross product is defined by a right-hand rule:

6.  orque  orque  orque  orque  orque  orque  orque  orque  orque 11-2 Vector Cross Product; Torque as a Vector The cross product can also be written in determinant form:

7.  orque  orque  orque  orque  orque  orque  orque  orque  orque 11-2 Vector Cross Product; Torque as a Vector Some properties of the cross product:

8.  orque  orque  orque  orque  orque  orque  orque  orque  orque 11-2 Vector Cross Product; Torque as a Vector Torque can be defined as the vector product of the force and the vector from the point of action of the force to the axis of rotation:

9.  orque  orque  orque  orque  orque  orque  orque  orque  orque 11-2 Vector Cross Product; Torque as a Vector For a particle, the torque can be defined around a point O: Here, is the position vector from the particle relative to O.

10.  orque  orque  orque  orque  orque  orque  orque  orque  orque Example 11-6: Torque vector. Suppose the vector is in the xz plane, and is given by = (1.2 m) + 1.2 m) Calculate the torque vector if = (150 N). 11-2 Vector Cross Product; Torque as a Vector