1. Changing momentum: curving motion
Parallel component
(Along trajectory)
Rate of change of direction
Perpendicular component
(to trajectory)
Remind – p is a function of time, and both |p| and p^ may also depend on time.
Direction of motion in point A A

2. Rate of change of direction
Length of path A = vt
Similar triangles
Angle =
For small angle:
Direction:
For small angles is
perpendicular to
This is now done in the same order and the same way as in new (black) version of the book
is directed toward the
center of the kissing circle
- Normal to the path toward center of the “kissing” circle

3. The Momentum Principle for componentsA
Direction of motion in point A
Parallel component:
Perpendicular component:

4. The Momentum Principle for componentsA
Direction of motion in point A
Parallel component:
Perpendicular component:
Discuss briefly:
The magnitude is changed only if there is a force component along path
The direction is changed only if there is force component perpendicular to path
Rate of change of magnitude p Rate of change of direction of p

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

6. Example: the Moon and the Earth
Mass of the Moon: mm = 7×1022 kg
Distance from the Earth: R = 4×108 m
Period: T = 28 days
Mass of the Earth: mE = 6×1024 kg
Question: FEarth on M=? R mE mM
Solution:
From motion path:
Discuss the fact that following motion we can determine dp/dt, and if we know dp/dt we know that there was interaction and we can deduce what was the force. However, nature of the interaction (force) does not matter. And vice versa – if we know force we can predict motion.
any force
motion of any object
these are not the same things!
This is precise – works at any speed!