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Understanding Vector Product in Angular Rotation: Theory and Application

Learn how to calculate vector products, cross products, and rotational dynamics in this comprehensive guide. Dive into right-hand rule, determinate method, and the connection between rotational and translational motion.

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Understanding Vector Product in Angular Rotation: Theory and Application

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  1. Chapter 10 More with angular rotatoin

  2. Cross product(Vector Product) • The solution of a vector product AxB is a vector in a direction that is perpendicular to the two vectors A and B. (Right hand rule) • A X B = -B X A • [A XB] = AB sin (theta) • ixj =-jxi = k • jxk = -kxj = i • kxi = -ixk = j • ixi = jxj = kxk = 0

  3. A x B = (Axi+ Ayj + Azk) x (Bxi+ Byj+ Bzk) = (Ay Bz - Az By )i = (AzBx - AxBz) j = (AX BY - AYBX) K

  4. Determinate method (Ay Bz - Az By )i + (AzBx - AxBz) j + (AX BY - AYBX) k

  5. Relating rotational with translational • Linear momentum • Torque

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