KPE 263 Biomechanics Week 4: Angular Kinematics

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Questions and Answers

What are the main types of motion described in biomechanics?

The main types of motion in biomechanics are linear motion, angular motion, and general motion.

How do absolute angles differ from relative angles in angular kinematics?

Absolute angles are measured from a fixed reference, while relative angles are measured between two moving segments.

Define angular displacement and its significance in biomechanics.

Angular displacement is the change in angle of a rotating body and is significant as it quantifies rotation during motion.

What is angular velocity, and how is it different from angular acceleration?

Angular velocity is the rate of change of angular displacement over time, while angular acceleration is the rate of change of angular velocity. Signup and view all the answers

In biomechanics, what role does the study of kinematics play?

Kinematics studies the motion of bodies without considering the forces causing the motion. Signup and view all the answers

How do you define absolute angle in angular position, and provide an example?

An absolute angle is the orientation of a line segment in space with respect to a fixed reference axis. An example is the instantaneous angle of the thigh segment relative to the horizontal axis fixed to the earth. Signup and view all the answers

What is the difference between absolute and relative angles?

Absolute angles refer to measurements concerning a fixed reference axis, while relative angles are measured in relation to a movable reference axis. For instance, the angle of the tibia with respect to the femur during running is a relative angle. Signup and view all the answers

How is the tangent of an angle calculated using coordinates?

The tangent of an angle $ heta$ can be calculated using the formula $tan( heta) = \frac{y_{prop} - y_{distal}}{x_{prop} - x_{distal}}$. This relates the vertical and horizontal components of a segment. Signup and view all the answers

Why is it important to distinguish between absolute and relative angular positions in biomechanics?

Distinguishing between the two helps accurately analyze and assess biomechanics, as movements can differ significantly depending on the fixed or movable reference. This is essential for understanding joint mechanics and optimizing performance. Signup and view all the answers

Given the calculation $tan^{-1}(0.22)$, what is the value of angle θ?

The value of angle θ is approximately $12.53°$. This is found by taking the inverse tangent of the given value. Signup and view all the answers

Define angular displacement and provide the equation used to calculate it.

Angular displacement is the change in position from the initial angular position, calculated using the equation $\Delta \theta = \theta_2 - \theta_1$. Signup and view all the answers

What is the significance of the axis of rotation in angular motion?

The axis of rotation is the line that is perpendicular to the plane of rotation, indicating the center around which all parts of a rigid body rotate. Signup and view all the answers

What are relative angles and how are they determined in the context of two distinct segments?

Relative angles are the angles created by the longitudinal axes of two distinct segments, such as the knee and thigh in the sagittal plane. Signup and view all the answers

Explain angular velocity and its calculation method.

Angular velocity (ω) is the rate of change of angular position, calculated using the formula $\omega = \frac{\theta_2 - \theta_1}{t_2 - t_1}$. Signup and view all the answers

What mathematical formula is used to find relative angles between segments?

The Law of Cosines is used, represented as $a^2 = b^2 + c^2 - 2bc \cos A$. Signup and view all the answers

Describe angular acceleration and its formula.

Angular acceleration (α) measures the change in angular velocity over time, calculated with the formula $\alpha = \frac{\omega_2 - \omega_1}{t_2 - t_1}$. Signup and view all the answers

What units are used to measure angles in relation to angular motion?

Angles in angular motion are measured in radians, which relate the arc length to the radius of the circle. Signup and view all the answers

In the formula $a^2 = b^2 + c^2 - 2bc \cos A$, what do the variables represent?

The variables $a$, $b$, and $c$ represent the lengths of the sides of a triangle, and $A$ is the angle opposite side $a$. Signup and view all the answers

How can the knee flexion angle be defined using relative angles?

The knee flexion angle is the angle between the thigh and the leg when viewed from the sagittal plane. Signup and view all the answers

In the context of angular motion, what does the term 'transverse plane' refer to?

The transverse plane refers to the horizontal plane where motion occurs around a vertical axis of rotation. Signup and view all the answers

How does angular motion differ from linear motion?

Angular motion involves rotation around an axis, where all parts of a body may move through the same angle but varying linear displacements, while linear motion involves movement along a straight path. Signup and view all the answers

What type of calculations are involved in determining the angular position (θ) in biomechanics?

Calculating angular position involves using the positions of the segments, often through distance formulas or trigonometric functions. Signup and view all the answers

What role does angular kinematics play in biomechanics?

Angular kinematics studies the motion of bodies in rotation without considering the forces causing the motion, essential for analyzing the movement of limbs and joints. Signup and view all the answers

Why are relative angles important when analyzing human movement?

Relative angles help in accurately describing the movements of different segments, which is crucial for injury prevention and rehabilitation. Signup and view all the answers

What is the significance of the absolute angle in comparison to relative angles?

Absolute angles provide a fixed position reference for each segment, while relative angles indicate their position relative to each other. Signup and view all the answers

How would you compute the relative angle given coordinates for two segments, say a hip and an ankle?

You would use the distance formula: $\text{distance} = \sqrt{(x_{hip} - x_{ankle})^2 + (y_{hip} - y_{ankle})^2}$ to determine the positions first. Signup and view all the answers

How many degrees are there in one radian?

There are approximately 57.3 degrees in one radian. Signup and view all the answers

What is the relationship between revolutions and degrees?

One revolution equals 360 degrees. Signup and view all the answers

Define absolute angle in terms of a line segment's orientation.

An absolute angle is the orientation of a line segment in space, typically measured from a fixed reference line. Signup and view all the answers

What formula is used to calculate the tangent of an angle (θ) based on coordinates?

The formula is $\tan(\theta) = \frac{y_{prox} - y_{dist}}{x_{prox} - x_{dist}}$. Signup and view all the answers

In an example, if $y_{prox} = 0.83$, $y_{dist} = 0.61$, $x_{prox} = 0.24$, and $x_{dist} = 0.53$, what would be the tangent of angle θ?

The tangent of angle θ would be approximately $\tan(\theta) = \frac{0.83 - 0.61}{0.24 - 0.53} = 0.37$. Signup and view all the answers

What is the significance of measuring instantaneous angles in biomechanics?

Measuring instantaneous angles is important for analyzing body movements and optimizing performance. Signup and view all the answers

How do you find the angle θ from its tangent value?

To find angle θ, use the formula $\theta = \tan^{-1}(\text{tan(θ)})$. Signup and view all the answers

If the tangent of angle θ equals 0.37, what is θ approximately equal to?

θ is approximately equal to $\tan^{-1}(0.37)$, which is around 20.3 degrees. Signup and view all the answers

What is the expression used to calculate side 'a' in a triangle when given sides 'b', 'c', and angle 'A'?

The expression is $a^2 = b^2 + c^2 - 2bc \cos A$. Signup and view all the answers

If side 'b' measures 0.32m and side 'c' measures 0.31m, what is the computed value of $b^2 + c^2$?

The computed value is $0.32^2 + 0.31^2 = 0.1024 + 0.0961 = 0.1985$. Signup and view all the answers

In the expression for calculating side 'a', what role does angle 'A' play?

Angle 'A' affects the value of $\cos A$, which adjusts the length of side 'a' based on the triangle's angle configuration. Signup and view all the answers

What does 'C' represent in the context of the provided formulas?

'C' is typically used to denote the angle opposite side 'c' in a triangle. Signup and view all the answers

Explain what the negative cosine indicates in the Law of Cosines formula.

The negative cosine indicates the angular relationship and adjusts the resulting length based on the angle's size. Signup and view all the answers

If the calculated angle 'A' equals -90°, what can you infer about the triangle?

A triangle with angle 'A' equal to -90° suggests that it is not physically feasible because angles cannot be negative in a triangle. Signup and view all the answers

What is the significance of the sides measuring 0.45m, 0.32m, and 0.31m in the problem context?

These side lengths are crucial for applying trigonometric principles to find unknown angles or side lengths in the triangle. Signup and view all the answers

How do you derive angle A from the Law of Cosines once side a is calculated?

Angle A can be derived using $A = \cos^{-1}\left( \frac{b^2 + c^2 - a^2}{2bc} \right)$ after side 'a' is known. Signup and view all the answers

Flashcards

Biomechanics

The study of the structure and function of biological systems by means of the methods of mechanics.

Angular Kinematics

The branch of biomechanics that studies the motion of objects in rotation, such as joints and limbs.