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# MOMENTUM - PowerPoint PPT Presentation

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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Presentation Transcript

• 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;

• 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)

• 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