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.

Chapter 11Angular Momentum; General Rotation

11-2 Vector Cross Product; Torque as a Vector11-3Angular Momentum of a Particle11-4 Angular Momentum and Torque for a System of Particles; General Motion11-5 Angular Momentum and Torque for a Rigid Object11-6 Conservation of Angular Momentum14-1 Simple Harmonic Motion

HW#9:Chap.11:Pb.11, Pb.21, Pb.24, Pb.32,Pb.41, Pb.51Due Wednesday, Dec. 3 after Thanksgiving break

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Motion of Rolling Objects

For the solid ball For the hollow ball

• Rolling objects have rotational and translational Kinetic Energy

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m• 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

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m• 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

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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:

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11-2 Vector Cross Product; Torque as a Vector

The cross product can also be written in determinant form:

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11-2 Vector Cross Product; Torque as a Vector

Some properties of the cross product:

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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:

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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.

r

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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

r

Fr