Angular Kinematics & Motion Notes

Angular Kinematics & Uniform Circular Motion

  • Overview

    • Chapters covered: Linear Kinematics (Chapter 9), Angular Kinematics (Chapter 10), Linear Kinetics (Chapter 11), and Angular Kinetics (Chapter 12).

Kinematics vs Kinetics

  • Kinematics:

    • Studies spatial and temporal components of motion.

    • Key components:

    • Linear position (P), velocity (V), and acceleration (A).

    • Angular position (Θ), velocity (ω), and acceleration (α).

    • Time (t) is also a crucial element.

  • Kinetics:

    • Focuses on the causes of motion.

    • Includes forces, torque, impulse, momentum, work, power, and energy.

Angular Motion

  • Definition:

    • Represents rotation; different regions of an object travel different linear distances over the same time frame.

    • Points on the axis of rotation remain stationary unless there is general motion.

  • Types of Rotation:

    • Pure Rotation: No linear motion of the axis of rotation.

    • General Motion: Describes simultaneous rotation and translation.

Angular Kinematics

  • Angle Measurements:

    • Units employed: Degrees (°) and Radians (rad).

    • 1 radian = 57.3°, translating the arc length to radius.

  • Angular Position (Θ):

    • Vector orientation relative to the positive x-axis.

    • In the x,y plane, the axis for the vector is the z-axis, e.g., θ = 30°k.

  • Angular Displacement (ΔΘ):

    • Defined as Δθ = θf - θi.

    • Angular distance is the length of the path traveled.

  • Angular Velocity (ω) & Acceleration (α):

    • Angular velocity: ω = Δθ/Δt.

    • Angular acceleration: α = Δω/Δt.

    • Positive ω does not guarantee positive α; instantaneous values occur as Δt approaches 0.

Angular Speed

  • Definition:

    • Scalar amount representing how fast an object rotates, always positive.

    • Distinction between Instantaneous Angular Speed (some ω) and Average Speed.

Segment Angles

  • Define the orientation of a body segment, typically from the horizontal axis at the distal end.

  • Measured using right triangles with joint coordinates (shoulder, elbow, wrist).

Biceps Curl Example

  • During a full repetition, observe:

    • Changes in forearm angle, angular velocity, and angular acceleration throughout the movement.

    • Angular changes are influenced by time to complete the action and the mass of weights involved.

Joint Angles

  • Defined by one segment relative to another.

    • Included Angle: Decreases when the joint closes (flexion).

    • Excluded Angle: Increases when a joint opens (extension).

  • Useful to calculate included elbow joint angles by knowing proximal and distal segment angles.

Linear and Angular Relationships

  • Relationships outlined about angular velocity (ω) and linear velocity (v), with reference to radius (r).

  • Centripetal and centrifugal accelerations distinguish between the inward versus outward directional forces.

Path Dynamics in Biceps Curl

  • Examination of how repetition speed and lengths of forearm and hand affect the angular and linear properties of movement.

Important Equations

  • Angular properties linked to linear characteristics.

  • v = ω·r, where the point of contact is momentarily stationary during rolling without slipping.