MOMENTUM l Momentum is a measure of motion =“magnitude of motion”, “impetus”, “impulse” p = m  v rate of change of momentum = force: if no force acts,

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Presentation transcript:

MOMENTUM l 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 extended bodies, or systems of bodies, can have “translational” or “rotational” motion rotational motion = movement around a straight line, the “axis of rotation” l 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  r 2 ) 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 l 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