L19 - Angular Kinetics Intro: Generating Rotation; Torque

• How to run fast:

  • But first… How do we generate the appropriate forces?
  • Rotational effects of force
  • Effect of mass & mass location
  • Timing
  • How do we control the motion such that forces are applied at the appropriate times & directions?
  • All internal forces on body are rotational - torques & rotations
• Force is generated by contraction of muscle but causes rotations of segment:

  • Thus far we have talked about external forces that cause linear motion to the centre of mass
  • But what about the forces that cause rotation in human motion because all internal forces are rotational!
• Force is generated by contraction of muscle but causes rotations of segment:

  • When muscle applies force to joint creates/causes rotational force
  • External can have both rotational & linear force
  • When talking about rotational force → looking at torque
• The effect of force depends on the point & direction of application with respect to the CoM:

  • Force through the CoM
  • Generates a linear motion
  • F - m aCoM → CoM accelerates
  • A force through CoM generates linear motion only
  • Ball move forward in a linear direction (translation)
  • Not going to rotate/spin
  • Maintains its orientation
• The effect of force depends on the point & direction of application with respect to the COM:

  • Force NOT through the COM (eccentric force)
  • Angular motion (spin) is generated
  • Generates a linear motion
  • F - m aCoM → CoM accelerates
  • An eccentric force generates both linear & angular motions
• The effect of force depends on the point & direction of application with respect to the COM:

  • Force NOT through the COM (eccentric force)
  • Ball will rotate, change its orientation
  • Will also translate → components of force
  • General motion = some change in rotation & translation
  • How would you get it to spin & not translate
  • Apply forces in opposite directions that are off CoM - coupled → so can balance/spin
• The effect of force depends on the point & direction of application with respect to the COM:

  • Torque/momentum - change in rotation
  • Torque is the rotational effect of a force
  • Can also refer to that off centred/outside CoM force as eccentric force
• The effect of force depends on the point & direction of application with respect to the COM:

  • Torque/momentum - change in rotation
  • What can we do if we want more rotation from the force?
  • Magnitude of force is related to direction
  • Which torque rotation effect we see need to apply force off centre: important components in magnitude of rotation is where/distance from CoM apply the force + magnitude (the lever) - the more turning effect the force has
• Example of this is a door:

  • Rotate door around hinge
  • Put handle as far away from hinge
  • Increase distance
  • Gives greater mechanical advantage
• Important Info about Torque:

  • Torque is influenced by:
  • Magnitude of the force
  • Line of action of the Force (direction)
  • Point of application of the force
• Important Info about Torque:

  • Point of application of the force
  • Where force is applied
  • How far away from rotation/CoM
  • Only perpendicular plane of motion will cause rotation
  • If not perpendicular got to use sin(𝜽)
  • Compression force hold joint together
  • Related to how much force pull
• Important Info about Torque:

  • Point of application of the force
  • Force to cause rotation - going upward
  • Elbow force one way, load other way why hard at start of bicep curl - when gets closer to perpendicular/elbow becomes easier as all muscle force is causing rotation
  • Work harder to initiate movement
  • Only perpendicular component cause rotation
• Torque:

  • Ƭ = Fr sin(𝜽)
  • r = distance from CoM (units = m)
  • Torque = N/m
  • If given mass/weight got to convert to Newtons (N)
• Torque:

  • Ƭ = F * r sin(𝜽)
  • The distance r is always measure perpendicular - ie at right angles or 90° - to the line of action of the force
  • r = distance from CoR to point of application of force
  • r units = m
  • Torque = N/m
  • If given mass/weight got to convert to Newtons (N)
• Important Info about Torque:

  • The axis of rotation can be fixed
  • The hinges on a door
  • Your forearm is fixed to your elbow axis
  • Knee - as it rotates is dependent on width of hips
  • As bend joint slides back & forth & rotates
  • Screw home mechanism - 3D
  • Have to account for different directions
• Important Info about Torque:

  • The axis of rotation can be free
  • Centre of mass (CoM)
  • For sport performance eg high jumpers
  • Are creating rotation around CoM, something we created not a thing
  • Is changing all the time
• Which force has the greatest advantage?

  • 𝚃 = Fr
  • Torque = force x distance from axis of rotation
• Which force has the greatest advantage?

  • When talking about forces acting
  • Force of muscle & force of resistance how much muscle force is required
  • Done by torque equation (𝚃 = Fr)
  • Has direction forces is acting in
  • Need direction so use right hand rule → fingers in pos direction of force
  • Thumb = direction of torque vector
  • Fingers around plane of rotation
• Direction of Rotation & Torque Vector:

  • Right Hand Rule
  • Fingers in direction of force ie, direction of rotation
  • Thumb points in direction of torque vector (ie perpendicular to plane of rotation)
  • Counter ClockWise (CCW) = pos
  • ClockWise (CW) = neg
• What else can we do with this? - Bending Moment:

  • That any section (eg xs, xs) is equal to the force applied to the beam (F) multiplied by the distance of its point of application form that section (x)
  • Mbxs = F x
• What else can we do with this? - Bending Moment:

  • Cause to deform under that force
  • Falling on outstretched arm - bones bend lot of stress on bones, amount of stress related to central area of bone
  • How fractures can occur (foosh injury) - bone takes bending load that exceeds its tolerance
  • Torque nowhere to go so cause bone to bend
  • Bending moment in pole vaulting