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MOMENTUM . Momentum is a measure of motion =“magnitude of motion”, “impetus”, “impulse” p = m  v rate of change of momentum = force:

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  • Momentum
    • is a measure of motion =“magnitude of motion”, “impetus”, “impulse” p = m  v
    • rate of change of momentum = force:
    • if no force acts, then rate of change of momentum = 0 ; momentum of an object does not change if no force acts on it.
    • for a “system of objects”: total momentum does not change if there is no outside (net) force -- “conservation of momentum”
    • examples:
      • throwing ball from a boat
      • recoil from a gun
      • jet and rocket propulsion
      • collision: total momentum before collision = total momentum after collision;
rotational motion angular momentum
Rotational motion, angular momentum
    • extended bodies, or systems of bodies, can have “translational” or “rotational” motion
    • rotational motion = movement around a straight line, the “axis of rotation”
  • quantities relevant to describe rotational motion:
    • “angular velocity”  (= rate of change of angle) number of turns per unit time
    • moment of inertia describes how mass is distributed with respect to rotation axis I = Sum (m  r2)
    • angular momentum: L =  I (note that formulae above only correct in simplest case, i.e. rotation of symmetric body around its symmetry axis)
    • “torque” = force x lever arm; lever arm = distance between center (axis) of rotation and line of action of the force;
    • torque = 0 if no force, or if force acts on center of rotation (e.g. pushing at center of wheel does not make wheel rotate, but pushing at wheel's rim does)
conservation of angular momentum
Conservation of angular momentum
  • conservation of angular momentum
    • the total angular momentum of a rigid body or a system of bodies is conserved (does not change) if no outside torque acts on the system;
    • note: angular momentum is a vector - direction of axis of rotation makes a difference
    • “angular momentum is conserved” means both magnitude and direction of rotation is constant
    • if torque acts, then angular momentum changes: change in rotational speed, or direction of rotation, or both; change of axis of rotation is perpendicular to torque (precession)
    • examples:
      • pirouette of ice skater
      • diver doing somersault
      • motion of planets around Sun
      • riding a bike
      • gyroscope
      • Earth's axis of rotation