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MOMENTUM

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

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  1. MOMENTUM • 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;

  2. 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)

  3. 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

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