KPE 263 Biomechanics Week 4: Angular Kinematics

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

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

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

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

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

<p>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.</p> Signup and view all the answers

<p>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.</p> Signup and view all the answers

<p>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.</p> Signup and view all the answers

<p>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.</p> Signup and view all the answers

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

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

<p>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.</p> Signup and view all the answers

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

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

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

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

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

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

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

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

<p>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.</p> Signup and view all the answers

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

<p>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.</p> Signup and view all the answers

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

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

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

<p>There are approximately 57.3 degrees in one radian.</p> Signup and view all the answers

<p>One revolution equals 360 degrees.</p> Signup and view all the answers

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

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

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

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

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

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

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

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

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

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

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

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

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

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