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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