Angular Kinematics Relationships.pptx Biomechanics II by Susan J. Hall DPT 4th Semester

Angular Kinematics Relationships Biomechanics II by Susan J. Hall DPT 4th Semester

1. Angular Kinematics Relationships By Dr. Basil Wahab PT August 2024

2. Angular Kinematics Angular motion occurs when all points on an object move in circular paths about the same fixed axis.

3. What is an angle? An angle is formed by the intersection of two lines. The symbol for angle is θ (Theta). Angles can be measured in degrees or radians ( rads ). 1 rad = 180/Pi = 57.30

4. Types of Angles measured in Biomechanics Relative angle : Angle of a joint formed between the longitudinal axes of adjacent body segments Anatomical reference position Absolute angle : Horizontal reference Vertical reference

5. Angular Displacement Angular displacement is the change in angular position experienced by a rotating line. A vector quantity.

6. Link between Linear Distance & Angular Displacement Radius is the link between linear and angular kinematics If the angular displacement is measured in radians, then the linear distance (arc length) is equal to the angular displacement times the radius. L = ∆ θ x r

7. Angular Velocity The rate of change of angular displacement. Average angular velocity equals angular displacement divided time. ω = ∆ θ / ∆t The symbol is ω (omega). Angular velocity is a vector found using the rt. hand rule.

8. Angular Distance and Angular Speed Angular distance and angular speed define a magnitude of rotation but no direction as they are scalar quantities .

9. Link between Linear and Angular Velocity The link is radius. All points on a golf club undergo the same angular displacement and therefore the same angular velocity. But they trace out different arc lengths based on their radius, therefore their linear velocities must be different.

10. Points on Golf Club

11. New (and convenient) Reference Frame

12. Angular Acceleration The rate of change of angular velocity. Average angular acceleration equals the change in angular velocity divided by time. ἀ = ∆ ω / ∆t The symbol is ἀ (alpha) Angular acceleration is a vector found using the rt. hand rule.

13. Direction of an angular vector Not like linear vectors. Angular vectors are perpendicular to the plane of motion. Must use right hand rule — Curl fingers of rt. hand in the direction of rotation. — The direction of your extended thumb is the direction of the angular displacement vector. A counterclockwise finger curl means the thumb is pointing in the positive direction

14. Angular Acceleration Angular acceleration occurs when something spins faster and faster or slower and slower, or when the object's axis of spin changes direction.

15. Linear Acceleration and Rotation When an object has angular motion, it is often easier to express linear acceleration relative to a reference frame that moves with the object. So, instead of describing acceleration in the fixed X and Y directions, we consider... Centripetal (radial) acceleration — Calculated using angular velocity Tangential acceleration — Calculated using angular acceleration

16. Centripetal Acceleration The component of linear acceleration directed towards the axis of rotation (center of the circle). Associated with the change in direction of an object moving in a circle. Changes the direction of the velocity vector (arrow).

17. Tangential Acceleration The component of linear acceleration tangent to the circular path (perpendicular to the radius). Associated with the speeding up of an object moving in a circle. Increases the length of the tangential velocity arrow. Equal to the angular acceleration times the radius.

18. Angular Kinematics Summary Angular Linear

19. THANK YOU !