ESS 3301 Lec 8 - Newtons Laws Angular

# ESS 3301 Lec 8 - Newtons Laws Angular - Announcements...

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Announcements Announcements Last day to drop Monday, Oct 31 Problem Sets are out there…get busy Exam 2 is Thursday, Oct 20

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Newton’s Laws Governing Newton’s Laws Governing Angular Motion Angular Motion ESS 3301-003 Lecture 8 Reading: McGinnis, Ch. 5, 6, 7
Force Application and Force Application and Resulting Motion Resulting Motion 1. A force is applied through the center of an object which is not fixed in any way… Result: Translation 1. A force is applied and the object is fixed on an end, and otherwise free to move… Result: Rotation about the fixed or pinned axis 1. A force is applied at a point and in a direction not through the center…again the object is not fixed… Result: Rotation about center of mass

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Angular Motion Angular Motion Linear Motion Motion in a straight line or curvilinear path Rectilinear Curvilinear Angular Motion Motion of a point or object about an axis of rotation (fixed or translating) All points of a body move through the same angular path but not necessarily through the same distance Doesn’t have to complete the “circle”
Part 1 Part 1 Angular Motion, Angular Angular Motion, Angular Kinematics and Kinetics Kinematics and Kinetics

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Angular Motion Angular Motion
Rotation versus Translation Rotation versus Translation

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Instantaneous Center Instantaneous Center of Rotation of Rotation In machines - Center of rotation is usually fixed Not the case with humans Asymmetries at joints Bone displacement during movement (e.g. tibia and femur) e.g. knee joint center vs. lateral condyle So what do we do? 1) Assume a static instantaneous joint center 2) Place markers on the segment rather than at the joint center, then calculate the instantaneous joint center Intersection of the 2 segments (e.g. tibia and femur) Motion of one segment relative to some fixed marker (e.g. humerus to acromion process) r r
Angles Angles Angle Marked by the intersection of two lines or planes Units of Measure Degrees (arbitrary units) Radians (fundamental ratio) Revolutions (one revolution = 360 o ) 360º = 2π radians = 1 revolution 45 o Vertex

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Radians Radians One radian is the angle at the centre of a circle described by an arc equal to the length of the radius Circumference of a Circle = 2π r because there are 2π radians in 360 o radian r s 1 = = θ If s = r, then θ is 1 radian
Angular Motion Vectors Angular Motion Vectors Right Hand Thumb Rule Used to show the direction of angular motion General “rule of thumb”

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Angular Position & Displacement Angular Position & Displacement Angular Position Defines an object’s position relative to a defined spatial reference system Angular Displacement Defines the change in angular position “Vector” quantity (arrow) Final angular position minus initial angular position If final position is 35º and the initial position is 70º, then what is the angular displacement?
Angular Velocity ( Angular Velocity ( ω ω ) ) t time time time in

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