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## PowerPoint Slideshow about 'MOMENTUM' - winslow

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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:
- 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 quantities relevant to describe rotational motion:

- extended bodies, or systems of bodies, can have “translational” or “rotational” motion
- rotational motion = movement around a straight line, the “axis of rotation”

- “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
- 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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