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Questions and Answers
A person walks along a straight path to a river's edge at a 60° angle. If the direct distance to the river is 200 yards, how far must the person walk along the path to reach the river's edge?
A person walks along a straight path to a river's edge at a 60° angle. If the direct distance to the river is 200 yards, how far must the person walk along the path to reach the river's edge?
- $200 / \sin(60^\circ)$ yards
- $200 \cdot \cos(60^\circ)$ yards
- $200 / \cos(60^\circ)$ yards (correct)
- $200 \cdot \sin(60^\circ)$ yards
Which of the following statements accurately describes the commutative law of vector addition?
Which of the following statements accurately describes the commutative law of vector addition?
- The associative law is a specific case of the commutative law.
- Vectors can only be added if they have different units of measure.
- The sum of three or more vectors depends on the order in which the vectors are added.
- The sum of two vectors is independent of the order in which they are added, such that A + B = B + A. (correct)
What is the resultant vector when a vector is added to its negative?
What is the resultant vector when a vector is added to its negative?
- A vector with the same magnitude but opposite direction of the original vector.
- A vector with zero magnitude. (correct)
- A vector perpendicular to the original vector.
- A vector with twice the magnitude of the original vector.
If vector A has a magnitude of 5 units and points east, and vector B has a magnitude of 3 units and points west, what is the magnitude and direction of the resultant vector A - B?
If vector A has a magnitude of 5 units and points east, and vector B has a magnitude of 3 units and points west, what is the magnitude and direction of the resultant vector A - B?
A scalar of -2 is multiplied by a vector A with a magnitude of 4. What is the magnitude and direction of the resulting vector?
A scalar of -2 is multiplied by a vector A with a magnitude of 4. What is the magnitude and direction of the resulting vector?
A force vector is applied to an object. Which of the following characteristics does NOT fully define this force vector?
A force vector is applied to an object. Which of the following characteristics does NOT fully define this force vector?
The line of action of a force vector is best described as:
The line of action of a force vector is best described as:
If a force vector is represented with a length of 5 cm on a diagram where the scale is 1 cm = 20 N, what is the magnitude of the force?
If a force vector is represented with a length of 5 cm on a diagram where the scale is 1 cm = 20 N, what is the magnitude of the force?
In a Cartesian coordinate system, which elements are essential for defining a frame of reference?
In a Cartesian coordinate system, which elements are essential for defining a frame of reference?
When using a polar coordinate system to define a point in space, what two parameters are required?
When using a polar coordinate system to define a point in space, what two parameters are required?
Which of the following biomechanical elements can be represented using vectors within a frame of reference?
Which of the following biomechanical elements can be represented using vectors within a frame of reference?
What does the orientation of a force vector describe?
What does the orientation of a force vector describe?
Why is defining a frame of reference important in biomechanics?
Why is defining a frame of reference important in biomechanics?
A point in the plane is described by the polar coordinates $(r, \theta) = (10.0 m, 120°)$. What are the implications of the angle measurement?
A point in the plane is described by the polar coordinates $(r, \theta) = (10.0 m, 120°)$. What are the implications of the angle measurement?
Given a right triangle, which trigonometric function relates the side opposite to an angle $\theta$ and the side adjacent to $\theta$?
Given a right triangle, which trigonometric function relates the side opposite to an angle $\theta$ and the side adjacent to $\theta$?
In a right triangle, if you know the lengths of all three sides, how do you find the measure of one of the acute angles?
In a right triangle, if you know the lengths of all three sides, how do you find the measure of one of the acute angles?
In the component approach to analyzing motor skills, what is a common observation regarding the maturity levels of different body segments during the execution of a skill like overhand throwing?
In the component approach to analyzing motor skills, what is a common observation regarding the maturity levels of different body segments during the execution of a skill like overhand throwing?
In a triangle, two angles are known to be 90 degrees and 60 degrees. What is the measure of the third angle?
In a triangle, two angles are known to be 90 degrees and 60 degrees. What is the measure of the third angle?
Why is qualitative analysis commonly used in motor skill assessment, and what primary benefit does it offer to practitioners?
Why is qualitative analysis commonly used in motor skill assessment, and what primary benefit does it offer to practitioners?
In what scenario would a quantitative motion analysis be MOST necessary over a qualitative approach?
In what scenario would a quantitative motion analysis be MOST necessary over a qualitative approach?
You are given a right triangle and know the lengths of the two legs (the sides adjacent to the right angle). Which theorem allows you to calculate the length of the hypotenuse?
You are given a right triangle and know the lengths of the two legs (the sides adjacent to the right angle). Which theorem allows you to calculate the length of the hypotenuse?
In polar coordinates, if $\theta = 30°$, what does the value of sin(30°) = 0.5 represent in terms of the sides of a right triangle?
In polar coordinates, if $\theta = 30°$, what does the value of sin(30°) = 0.5 represent in terms of the sides of a right triangle?
Which of the following BEST distinguishes a scalar quantity from a vector quantity?
Which of the following BEST distinguishes a scalar quantity from a vector quantity?
A ladder leans against a wall, forming a right triangle. The ladder is 10 feet long, and the base of the ladder is 6 feet from the wall. What trigonometric function can be used to find the angle between the ladder and the ground?
A ladder leans against a wall, forming a right triangle. The ladder is 10 feet long, and the base of the ladder is 6 feet from the wall. What trigonometric function can be used to find the angle between the ladder and the ground?
If a biomechanics researcher is studying the effect of different running shoes on ground reaction force, would they be measuring a scalar or vector quantity, and why?
If a biomechanics researcher is studying the effect of different running shoes on ground reaction force, would they be measuring a scalar or vector quantity, and why?
A person stands some distance from a building. The angle of elevation to the top of the building is 60 degrees, and the height of the building is 100 feet. Which equation can be set up to find the distance from the person to the base of the building?
A person stands some distance from a building. The angle of elevation to the top of the building is 60 degrees, and the height of the building is 100 feet. Which equation can be set up to find the distance from the person to the base of the building?
Why are arrows used to represent forces in free-body diagrams?
Why are arrows used to represent forces in free-body diagrams?
A coach observes that an athlete consistently decelerates excessively during the later phase of a sprint. Using qualitative analysis, what would be the MOST effective initial step for the coach?
A coach observes that an athlete consistently decelerates excessively during the later phase of a sprint. Using qualitative analysis, what would be the MOST effective initial step for the coach?
Which of the following scenarios illustrates the concept of inertia?
Which of the following scenarios illustrates the concept of inertia?
If the scalar multiplication of a vector A by a scalar results in -9A, what does this imply about the scalar?
If the scalar multiplication of a vector A by a scalar results in -9A, what does this imply about the scalar?
Given two vectors, A and B, what is always true of the resultant vector C in the cross product A x B = C?
Given two vectors, A and B, what is always true of the resultant vector C in the cross product A x B = C?
In graphical vector analysis, what is the 'resultant' vector?
In graphical vector analysis, what is the 'resultant' vector?
What is the primary purpose of vector resolution?
What is the primary purpose of vector resolution?
A force is applied to an object, causing it to move both horizontally and vertically. What do these components represent?
A force is applied to an object, causing it to move both horizontally and vertically. What do these components represent?
A vector is resolved into horizontal and vertical components. Relative to the x-axis, which component is considered parallel?
A vector is resolved into horizontal and vertical components. Relative to the x-axis, which component is considered parallel?
In vector composition, what does the 'resultant vector' represent?
In vector composition, what does the 'resultant vector' represent?
Forces can be applied to a system either simultaneously or sequentially. How does the timing of force application most directly affect vector composition?
Forces can be applied to a system either simultaneously or sequentially. How does the timing of force application most directly affect vector composition?
Which factor does NOT directly influence the complexity of vector composition?
Which factor does NOT directly influence the complexity of vector composition?
What characterizes colinear vectors?
What characterizes colinear vectors?
In the context of functional anatomy, how do muscle groups typically produce force?
In the context of functional anatomy, how do muscle groups typically produce force?
What does a larger Q angle deviation in females correlate with?
What does a larger Q angle deviation in females correlate with?
How do muscle forces relate to degrees of freedom (DOF) in motor control?
How do muscle forces relate to degrees of freedom (DOF) in motor control?
What is the primary role of muscle forces in motor development?
What is the primary role of muscle forces in motor development?
How does motor learning enhance muscle function?
How does motor learning enhance muscle function?
What is the role of quantitative and qualitative assessment of fitness and movement in pedagogy?
What is the role of quantitative and qualitative assessment of fitness and movement in pedagogy?
Flashcards
Component Approach
Component Approach
Different body segments mature at different rates in skill performance.
Qualitative Analysis
Qualitative Analysis
Visually analyze motion to rapidly isolate factors affecting performance.
Quantitative Analysis
Quantitative Analysis
Deeper understanding of why a system moves the way it does using numerical data.
Scalar Quantity
Scalar Quantity
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Mass
Mass
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Inertia
Inertia
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Vector Quantity
Vector Quantity
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Weight
Weight
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Direction (of a Force Vector)
Direction (of a Force Vector)
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Orientation (of a Force Vector)
Orientation (of a Force Vector)
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Point of Application (of a Force Vector)
Point of Application (of a Force Vector)
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Magnitude (of a Force Vector)
Magnitude (of a Force Vector)
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Line of Action
Line of Action
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Frame of Reference
Frame of Reference
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Vectors in Biomechanics
Vectors in Biomechanics
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Polar Coordinate System
Polar Coordinate System
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Vector Equality
Vector Equality
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Commutative Law of Vector Addition
Commutative Law of Vector Addition
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Associative Law of Vector Addition
Associative Law of Vector Addition
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Negative of a Vector
Negative of a Vector
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Vector Subtraction
Vector Subtraction
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SOHCAHTOA
SOHCAHTOA
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Inverse Trigonometric Functions
Inverse Trigonometric Functions
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Pythagorean Theorem
Pythagorean Theorem
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Trigonometric Ratios
Trigonometric Ratios
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Inverse Trigonometric Functions
Inverse Trigonometric Functions
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Tree Height Problem
Tree Height Problem
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What is y?
What is y?
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Scalar x Vector
Scalar x Vector
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Vector x Vector (Cross Product)
Vector x Vector (Cross Product)
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Cross Product Orientation
Cross Product Orientation
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Graphical Vector Analysis
Graphical Vector Analysis
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Resultant Vector
Resultant Vector
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Vector Resolution
Vector Resolution
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Component Vectors
Component Vectors
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Vector Composition
Vector Composition
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Colinear Vectors
Colinear Vectors
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Complexity Factors in Vector Composition
Complexity Factors in Vector Composition
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Q Angle (Quadriceps Angle)
Q Angle (Quadriceps Angle)
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Muscle Force Vector Convergence
Muscle Force Vector Convergence
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Muscle Force and Motor Control
Muscle Force and Motor Control
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Muscle Force and Motor Development
Muscle Force and Motor Development
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Muscle Force and Motor Learning
Muscle Force and Motor Learning
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Assessment in Pedagogy
Assessment in Pedagogy
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Study Notes
- Paradigms for studying motion of the system are explored in this document.
Qualitative Motion Analysis
- Qualitative Motion Analysis describes the body's appearance upon visual inspection during skill performance.
- It is subjective and relies on visual observation.
- This analysis includes assessing position in space, body parts relative to each other, and the position of segments of body parts relative to each other.
- Two general approaches to qualitative analysis exist: composite and component.
- The composite approach, also known as the total body approach, views the entire body as a system refining movement patterns through phases.
- The component approach uses the same phase/stage method but breaks the body down into component sections instead of viewing it as a global system.
Composite Approach
- Total body approach often goes by "developmental biomechanics".
- Movement patterns break into the primary body part.
- Stages of skill progression are based on the combination of all body parts.
- Each stage identifies important body parts used to perform the skill.
- The number of stages can vary based on the task requirements for a task.
- Total body composite approach can be applied to throwing, as demonstrated in a sequence of five stages.
- Stage 1 includes vertical wind-up, feet remaining stationary, and no spinal rotation.
- Stage 2, horizontal wind-up introduces block rotation and follow-through across the body.
- Subsequent stages involve increasingly complex movements, such as the addition of ipsilateral or contralateral steps, spinal rotation, and arm/leg follow-through.
Component Approach
- The component approach is referred to as the "error analysis strategy."
- The process involves observing each primary body component.
- Each body component has its own evaluative series of stages or phases
- Stages/phases can advance independently.
- Overhand throwing is broken down into component parts such as trunk, arms, and the feet.
- Performers demonstrate mature skill in one body part while other segments are at less mature levels.
- Qualitative and quantitative analyses act as complemenents.
- Qualitative analysis is commonly used, which improves the ability to visually analyze motion and rapidly identify performance factors.
Quantitative Motion Analysis
- Quantitative Motion Analysis comes from the need for deeper understanding of why a system moves the way it does.
- Performers/practitioners require more accurate data from quantitative measurement.
- Application examples include enhancing the performance of athletes and quantifying injury to improve treatment.
- Biomechanical research aims to understand human motion, optimize performance/equipment, and prevent injury.
- Scalar quantity possesses only a magnitude with no directional association.
- Mass exemplifies a scalar quantity, indicating the amount of matter and body inertia rather than direction.
- Inertia, an additional scalar quantity, denotes a body's resistance to changes in motion.
- Vector quantity requires both a magnitude of appropriate units and a precise direction.
- Weight serves as a vector example, illustrating how gravity pulls upon an object's mass, requiring both value and path.
Vectors Representing Forces
- Arrows represent forces in free-body diagrams because all forces exist as vectors.
- An arrow represents a vector quantity/force with a tip and tail, a scaled length, and imagined travel path.
- Direction applies as the way force enacts, e.g., going up, down, north, south, positive, or negative.
- Orientation is the vector's alignment measured counterclockwise from the positive x-axis, e.g., vertical, 45° from the horizontal.
- The point of application constitutes the system where force applies, defined by the vector's tail, such as at the toes or 2cm from the elbow's rotation axis.
- Magnitude measures size force depicted by vector length relative scale e.g. if 1cm = 10N that 10cm=100N
- Imaginary line of action goes infinitely over the vector through tip to tail.
Vectors in Frames
- An object's position can be defined using a Cartesian coordinate system.
- A Cartesian coordinate system refers to orthogonal axes passing through an origin to define space dimensions.
- Biomechanics uses defined points, segments (lines), and forces (vectors/arrows).
- Mathematic operations benefit from defining planes using polar coordination.
Polar Coordinate System
- The Polar Coordinate System has an origin and multiple referenced axes.
- Location is defined by the radius and the angle between points in between the reference axis and the point to the origin.
- Theta is often measured counterclockwise from x-axis.
- 0 = arctan (opposite side / adjacent side),
- SOHCAHTOA can be used to solve coordinate transforms.
- Pythagorean theorem can also be used as
- coordinate transform.
- Trigonometry uses lengths sides over given triangle.
Special Properties of Vectors
- Vectors have many properties, and can be used to understand physical examples such as:
- addition, subtraction, multiplication, etc..
- Can also understand one force, and multiple forces using graphical vector analysis
- Vector resolution, breaking a vector into components, reveals forces causing rise and run relative to horizontal/vertical axes.
- Vector composition sums vectors finding result force when multiple come upon an acting system.
- Forces applied combine simultaneously
- Colinear Vectors: vectors use the same line of actions
Connections:
- Rotary motion can be created via the rotary motion and stabilization provided by triceps in the elbow joint
- Q angle estimate femoral/tibalt alignment, and larger ones correlate directly with patellofemoral pain in females
- Motive forces for motor development allow voluntary controlled movement
- Constant practice in strength increases with variety and precision Quantitative and qualitative assessments of data give athletic programs accountability
- Data, such as fitness tests, provide accurate anatomic info, provide fundamental motor development tests, as well as provide movement task sheets
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Description
Test your understanding of vectors with these practice problems. Topics include vector addition, subtraction, scalar multiplication, and force vectors. Learn to calculate magnitudes, directions, and resultant vectors.
