Lecture 3: Motion in two and three dimensions (chap 4 in Halliday)

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Lecture 3 Motion in two and three dimensions
(chap 4 in Halliday)
To increasing the dimension is straightforward.
Just add more components on the vectors.
Position
Displacement
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Similarly, average velocity and instantaneous
velocity are defined as
Or simply
where
Same for acceleration
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Projectile motion (????) a special case of two
dimensional motion.

1. Vertical and horizontal motion are independent.
2. The horizontal motion has no acceleration, i.e.
   constant velocity.
3. Vertical motion is simply a linear motion (free
   fall) with constant acceleration discussed in
   lecture 1.

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1. 3,2,1
2. 1,2,3
3. Same
4. 6,5,4

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The gravity doesnt affect the result.
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Horizontal motion
Vertical motion
From the above, one has the equation of path
(trajectory)
x0 and y0 0
Horizontal range (R)
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Horizontal
Vertical
8

• vertical direction

• horizontal direction

eliminate t
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Uniform circular motion (????)

• The magnitude v of the velocity does not change,
  but the direction changes continuously.
• there is an acceleration

(?????)

• a always pointing towards to the center of the
  circle.

• the period is given by

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The magnitude of v is
5s
Since v1-v2, means that it completes half
circumference from 2s to 5s, therefore
2s
Average acceleration