Problems and solutions I

It follows then that 0 x x y y z z chapter

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ve to find the products of the basis unit vectors. Because of the antisymmetry property we get A ä A = 0. It follows then that `` `` `` 0 = x ä x = y ä y = z ä z. Chapter I - Rotational Dynamics and Equilibrium | 3 Using our definition of the cross product we can see that the cross product of two perpendicular unit vectors is a third unit vector perpendicular to the two. ` `` ` A ä B = A B sin q u ï v ä w = 1 ÿ 1 ÿ 1 u ` ` ` ` The cross product of the unit vectors x and y is thus a unit vector perpendicular to the xy plane. This is either z or -z. We insist that our coordinate system is right-handed; this means that `` ` x ä y = z. For the other combinations of unit vectors there is a simple rule to keep track of their cross products. Arrange x, y and z around a circle. x z y If the order of the three coordinates has the same sense of rotation as x, y, z it gains a positive sign. If opposite it gets a minus sign. `` ` `` ` y ä z = x, z ä x = y , `` ` `` ` `` ` y ä x = -z, x ä z = -y and z ä y = -x We can put all this together and get the cross product in terms of components. ` ` ` ` ` ` A ä B = I A x x + A y y + A z zM ä I B x x + B y y + B z zM ` ` ` = x I A y Bz - Az B y M + y H Az B x - A x Bz L + z I A x B y - A y B x M The determinant method is a common way to write this....
View Full Document

This document was uploaded on 02/26/2014 for the course PHYS 2425 at Blinn College.

Ask a homework question - tutors are online