L14 - Relationships bw/ Linear & Angular Kinematics

• Pi, Radians, Circumference:

  • Distance from centre of circle (origin) to outside = radius (r)
  • r is the same as the arc length = 1 rad
  • If go round twice of r around the circle = arch length = 2r
  • 2x the radius length = 2 rad
  • & the same for 3x = 3 rad
• Pi, Radians, Circumference:

  • Pi = ratio of arc length, & radius around 180°
  • Arc length = πr
  • Δ𝜽 = π rad
  • Δ𝜽 = 180°
  • π = 3.14
• Pi, Radians, Circumference:

  • Once go over 180° = π x r
  • Arch length = πr
  • Δ𝜽 = 2 π rad
  • Δ𝜽 = 360 °
• What is Pi?

  • Pi (π) is the ratio of a circle’s circumference to its diameter
  • Diameter = 2 * radius
• What is Pi?

  • If my arm is 78 cm, what distance do my fingertips travel after 180° abduction?
  • (π rad) * 0.78 m = 2.45 m or 3.14 * 0.78 m = 2.45 m
  • Multiply radiant by metres
  • What is the displacement of the finger tip?
  • (2) * 0.78 m = 1.56 m or 2 * 0.78 m = 1.56 m
• Radius & Arc Length:

  • The longer the radius the greater the arch length
  • Arc length = Δ𝜽r ← angle must be in radians!
  • If 𝜽 is in degrees, arch length = Δ𝜽r (π rad / 180°)
• Radius & Arc Length:

  • As increase radius increase arch length
  • Straight line = displacement
  • Still 40° but a’s arc length greater
  • than b's
  • Have to relate angular motion with linear motion
  • Relates angle to radius
  • Angular part is the arc length
  • If given angle & got to find arc length have to convert to radians
  • Angular to linear OR linear to angular got to be in radians!
  • How to get degrees to radians
  • Multiply by π radians / 180° (as equals 1 is the same as π rad)
  • π x r (if angle is 180°)
• Radius & Arc Length:

  • If given angle & got to find arc length have to convert to radians
  • Angular to linear OR linear to angular got to be in radians!!
  • How to get degrees to radians
  • Multiply by π radians / 180° (as equals 1 is the same as π rad)
  • π x r (if angle is 180°)
• Muscle Insertions Close to Joints:

  • Short change in muscle length produces a larger movement at the end limb
• Muscle Insertions Close to Joints:

  • a = end of limb or where force applied, b = muscle insertion
  • If want to move arm 40°
  • If radius in b is shorter doesn’t have to shorten as much
  • Tendons pretty close to axis of rotation as only shorten a certain amount
• Sports with Implements:

  • Increase speed of object by increasing its radius
• Sports with Implements:

  • Important implication for techniques
  • Can manipulate length of radius
  • End point is gong fastest
  • Assuming can change angle at same rate
• Angular Velocity & Linear Speed:

  • Angular velocity can produce linear velocity at the end of the limb
• Angular Velocity & Linear Speed:

  • Angular motion of club result in linear motion of the ball
  • d = arc length (special kind of distance)
  • 2 different ways could express distance

  1. Arc length
  2. Linear distance

  • 3rd equation = same as 2nd equation
  • d is = to change of angle r
  • Different way of expressing linear speed from angular motion (tangential speed)
  • Direction pull going to go from radius
  • Tangent to the circle