Angular Kinematics Notes

Angular Distance vs. Angular Displacement

• Angular Distance
  • Total length of angular path.
• Angular Displacement
  • Equal in magnitude to the angle difference between initial and final position of an object.
• Units
  • Example: Total from one swing is 85 degrees, and the finish is 30 degrees back.

Angular Kinematic Quantities

• The angular displacement at the elbow is zero when the forearm returns to its original position upon completing a curl exercise.

Units of Angular Measure

• 90 degrees = \frac{π}{2} radians = \frac{1}{4} revolution
• 180 degrees = π radians = \frac{1}{2} revolution
• 270 degrees = \frac{3π}{2} radians = \frac{3}{4} revolution
• 360 degrees = 2π radians = 1 revolution

Angular Speed vs. Angular Velocity

• Angular Speed
  • Angular distance / change in time.
• Angular Velocity
  • Angular displacement / change in time.
  • \frac{Af – Ai}{t2 – t1}
• Units
  • degrees/s or radians/s

Angular Acceleration

• Rate of angular velocity change with respect to time.
• \frac{Avf – Avi}{t2 – t1}
• Units
  • Degrees/s^2 or rad/s^2
• Average and instantaneous Angular Acceleration

Relationship between Linear and Angular Displacement

• Given a point on a rotating body and the axis of rotation:
  • linear displacement
• Curvilinear distance = radius of rotation * angular displacement
• Two conditions must be met (not specified in the transcript).

Linear and Angular Velocity

• Linear Velocity = Radius of rotation x angular velocity
• Two Components (not specified in the transcript)
• If angular velocity is constant:
  • RR = Linear Velocity
• If linear velocity is constant:
  • RR < angular velocity

Linear and Angular Acceleration Combined

• When an object accelerates along a curved path, it experiences both linear and angular acceleration simultaneously.
• Two components to consider:
  • Tangential acceleration
  • Radial Acceleration

Linear and Angular Acceleration

• Tangential Acceleration

  • Time rate change in linear velocity as it accelerates along a curved path.
  • Calculations
    • Tangential Acceleration = \frac{linear velocityf – linear velocityi}{change in time}
  • Increasing Linear (Tangential) Acceleration = radius of rotation x angular acceleration
    • Should be max just before release
    • Holding affect creates a radial acceleration tangentile point

• Radial Acceleration (AKA Centripetal Acceleration)

  • Rate of change in direction of a rotating body as it moves along a curved path.
  • Restraining Force
    • Centripetal Force (force towards the center)
    • Centrifugal Force (apparent outward force)
  • Radial acceleration Formula
    • \frac{(linear velocity)^2}{radius of rotation}
  • Gforce ride pulling force out restraining force to the center of axis restrain force that pulls in

• Small axis rotation greater centrifugal force larger axis smaller centrifugal force i.e. on a track to counter centrifugal force lean in to create centripetal force

• 180 Daytona Ave speed = 210.30 mph Michigan Top Speed = 196.23 mph Banking is higher increasing centripetal force