ECS221L7 - Position vector from point O to M: r = xi + yj +...

Info iconThis preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
    Rigid Bodies; Equivalent Force Systems Transmissibility Principle Force F is a sliding vector. = F F
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
    Vector (Cross) Product Multiply 2 vectors P × Q resulting in a vector. Define magnitude of product. Define direction of product.
Background image of page 2
    V = P × Q Magnitude: V = PQ sin θ , 0 < θ < π Direction: perpendicular to plane of P and Q Sense: determined by right hand rule θ V P Q
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
    Geometrical Meaning h=Q sin θ V = PQ sin θ = Ph = area of parallelogram formed by P and Q Q P h θ
Background image of page 4
    Properties Colinear : P × Q = 0 Non-commutative : P × Q = -Q × P Distributive: P × ( Q +R ) = P × Q + P × R Non-associative : (P × Q ) × R P × ( Q × R )
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
    Component Form i × i = 0 j × j = 0 k × k = 0 i × j = k k × i = j j × k = i P × Q = (P x i + P y j + P z k ) × (Q x i + Q y j + Q z k ) = (P y Q z -P z Q y )i + (P z Q x -P x Q z )j + (P x Q y -P y Q x )k j i k i k j
Background image of page 6
    Component Form by Determinants P × Q = = (P y Q z -P z Q y )i + (P z Q x -P x Q z )j + (P x Q y -P y Q x )k z y x z y x Q Q Q P P P k j i
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
    Position Vector
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 12
Background image of page 13
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Position vector from point O to M: r = xi + yj + zk x z y r M O Moment of a Force about a Point The moment of a force about point O is defined by: M O = r F (M = rF sin ) Units of moment are N m or, lb in r O F M o Moments in the Plane M O = r F M = rF sin = dF F r M o d F r M o d Varignons Theorem Moment of the resultant = Resultant of the moments r ( F 1 + F 2 + F 3 + ) = r F 1 + r F 2 + r F 2 Components of Moment r = xi + yj + zk F = F x i + F y j + F z k M O = r F = (yF z-zF y )i + (zF x-xF z )j + (xF y-yF x )k In the plane: M O = r F = (xF y-yF x )k...
View Full Document

Page1 / 13

ECS221L7 - Position vector from point O to M: r = xi + yj +...

This preview shows document pages 1 - 13. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online