# momentum

```MOMENTUM
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Momentum
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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
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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:
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“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
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conservation of angular momentum
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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
```