MOMENTUM

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