Grade 11Mechanics
If we are given r, p, and θ we can calculate the angular momentum of a particle from Eq. 10-2. Sometimes, however, we are given the components (x, y, z) of ![src=data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABUAAAAVCAIAAAAmdTLBAAAAd0lEQVQ4jc3SwQ2AIAwF0D9XB+o8nabLdBg9VBMErFSI8d96eHxKwDYXfOdNiMSm+pUB1q5XxmjKE5b1P2fB/m2WehMCAPg1z6na+M4rg8RcsRZTu3R0/6M16oy881HdeuUUr32WV96EEL9X7NP1V5/n//q/L7IDQtetPC5jvGoAAAAASUVORK5CYII=]()
and (x, y, z) of ![src=data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABgAAAAXCAIAAACeQxh6AAAAiUlEQVQ4je2SwRHAIAgEqYuCqIdqaIZiyEPNjAYVM+SX+7Muh2BJgR+UD1JGZE0AmZkQAMkMJARnGVD5RtFkduTmK1Cr/K5AGb1qlyBlBJIyWmoQAmQ1ZQS3l4VRc+jm6gunIKFhk9mdNqCHkNBexwMNQkHME9QJxZbagerJovFXC/2cDeht0kAXgnLgSroPTiIAAAAASUVORK5CYII=]()
instead. (a) Show that the components of ![src=data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAAaCAIAAAAIbfoLAAAAaklEQVQ4jWP4TzRgGORKb0+wsppwm1hTt6UxMKRtgyvdlsZAAKRtI91UKrkVDuBKb0+wQnEZHqVw1XAL8SmFBMSo0gFUSmxsEZ0G3n9///77e+ymwZVCFDkscDj//DwBpQ4LHIhR9///fwAEPreSYk9KNQAAAABJRU5ErkJggg==]()
along the x, y, and z axes are then given by
(b) Show that if the particle moves only in the xy plane, the resultant angular momentum vector has only a z component.
