Changing momentum curving motion A A Parallel component

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Changing momentum: curving motion A A Parallel component (Along trajectory) Rate of change of

Changing momentum: curving motion A A Parallel component (Along trajectory) Rate of change of direction Perpendicular component (to trajectory) A Direction of motion in point A

Rate of change of direction Length of path A = v t Angle =

Rate of change of direction Length of path A = v t Angle = For small angle: Similar triangles Direction: For small angles perpendicular to is is directed toward the center of the kissing circle - Normal to the path toward center of the “kissing” circle

The Momentum Principle for components A Direction of motion in point A Parallel component:

The Momentum Principle for components A Direction of motion in point A Parallel component: Perpendicular component:

The Momentum Principle for components A Direction of motion in point A Parallel component:

The Momentum Principle for components A Direction of motion in point A Parallel component: Rate of change of magnitude p Perpendicular component: Rate of change of direction of p

Example: the Moon and the Earth Mass of the Moon: Distance from the Earth:

Example: the Moon and the Earth Mass of the Moon: Distance from the Earth: Period: Question: m. M = 7× 1022 kg R = 4× 108 m T = 28 days =? R Solution: Parallel: =0 Perpendicular: What is the direction of ? m. M

Example: the Moon and the Earth Mass of the Moon: Distance from the Earth:

Example: the Moon and the Earth Mass of the Moon: Distance from the Earth: Period: Mass of the Earth: Question: mm = 7× 1022 kg R = 4× 108 m T = 28 days m. E = 6× 1024 kg FEarth on M=? R m. E m. M Solution: From motion path: any force motion of any object these are not the same things! This is precise – works at any speed!