SHMD 239 Kinesiology Unit 6

1. SHMD 239 KinesiologyUnit 6 Angular Motion

2. Angular Motion • Also known as rotation Definition: Occurs when a body moves on a circular path about a central line so that all parts of the body move through the same angle, in the same direction, in the same time

3. The same concepts and principles used to describe linear motion can be used to explain motion in a circle • Changes in position are measured by angles • The units of which are degrees (º) • This is measured with reference to something else – e.g. The ground, a vertical line form another object

4. Angular Distance • Angular Distance – the length of the path a body follows during motion • It is symbolised by the Greek letter phi (Ф)

5. Question: A gymnast does 2 ½ consecutive giant swings on a horizontal bar – that is, 2 ½ circles of the bar in an essentially straight or extended position Through what angular distance does the gymnast’s body pass in the process? (State your answer in degrees). ANSWER: 2 ½ circles Angular Distance = 360º + 360° + 180° = 900°

6. Angular Displacement • Angular Displacement – the difference between the starting position and the final position • It is symbolised by the Greek letter theta (θ)

7. Question: A gymnast does 2 ½ consecutive giant swings on a horizontal bar – that is, 2 ½ circles of the bar in an essentially straight or extended position (assume she is moving in a positive direction). What angular displacement does the gymnast’s body experience? (State your answer in degrees). ANSWER: Angular Displacement = 180°

8. Angular Speed • Angular speed of a rotating body is found by dividing the angular distance through which it has moved by the time taken: Angular Speed = Angular Distance / Time or, σ = Ф / t σ = Angular Speed Ф = Angular Distance t = Time Taken and is measured in degrees per second (º/s)

9. Question: It takes a girl on the balance beam 1.5s to swing her legs forward 120° and then backward 150°. What is the angular speed of her legs?(State your answer in degrees per second). ANSWER: Distance = 120° + 150° = 270° Time = 1.5s Angular Speed = Angular Distance / Time = 270° / 1.5s = 180°/s

10. Angular Velocity • Angular velocity – the rate of change of angular displacement Angular velocity is calculated in the same way as linear velocity – instead of displacement divided by time it is angular displacement divided by time

11. Angular velocity = Angular displacement / Time or, ω = θ / t • ω = Angular Velocity • θ = Angular Displacement • t = Time Taken • The symbol for angular velocity is the Greek letter omega (ω) and is measured in degrees per second (º/s)

12. Question: It takes a girl on the balance beam 1.5s to swing her legs forward 120° (from their initial position) and then backward 150° (to their final position). What is the angular velocity of her legs? (State your answer in degrees per second). ANSWER: Displacement = 120° + (-150°) = -30° Time = 1.5s Angular Speed = Angular Distance / Time = -30° / 1.5s = -20°/s

13. Home work Questions: • A gymnast does 3 consecutive giant swings on a horizontal bar – that is, 3 circles of the bar in an essentially straight or extended position. • Through what angular distance does the gymnast’s body pass in the process? (State your answer in degrees). • If it takes 2.0, 1.8, and 1.6 s to complete the first, second and third swings, respectively, what were the gymnast’s average angular speeds for each of these three parts of the total performance? • What was the average angular speed for the total performance? • If the angular velocity was 7 rad/s at the end of the first half swing and 4.5 rad/s at the end of the next half swing 1.2 s later, what was the gymnast’s average angular acceleration over that period?

14. End of Unit