Plane Curvilinear Motion

Plane Curvilinear Motion

0. Introduction
1. Rectangular Coordinates (x-y)
2. Normal and Tangential Coordinates (n-t)
3. Polar Coordinates (r-θ)

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Plane Curvilinear Motion

Position vector → Velocity vector → Acceleration vector

Position

Change in position
(displacement)

Reference frame

Origin Position vector Distance
(along curve)
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2

Plane Curvilinear Motion

Velocity

  lim r     r
v v dr

t0 t dt

Magnitude: v

Direction: tavn/g/enrtto the curve at that point

Note: v  r

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Plane Curvilinear Motion

Acceleration

  lim v     v
a a dv

t0 t dt

Magnitude: a

Direction: poain/t/ingvinward the curve

Note: a  v

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Plane Curvilinear Motion

1. Rectangular Coordinates (x-y)

2. Normal and Tangential Coordinates (n-t)
3. Polar Coordinates (r-θ)

Notes: Usage will depend on the situation
Usually, more than one can be used.
Sometimes, more than one is needed at the same time

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1.Rectangular Coordinates (x-y)

  xiˆ  yˆj
r

v  xiˆ  yˆj  vxiˆ  vy ˆj

  xiˆ  yˆj  vxiˆ  vy ˆj
a

Magnitude & Direction

- Pythagoras

r  x2  y2

v v 2  v 2
x y

a a 2  a 2
x y

- Trigonometry (sine and

cosine laws, etc.) 6
eg. tan   vy

vx

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1.Rectangular Coordinates (x-y)

Applications

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1. Rectangular Coordinates (x-
y)

Projectile Motion

y motion can be considered independently
from the x direction

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1.Rectangular Coordinates (x-y)

Example 1:

Notes:

Ans:

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1. Rectangular Coordinates (x-y)

Example 2: Projectile Motion

Ans:

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1. Rectangular Coordinates (x-y)

Example 3: Projectile Motion

Determine the smallest angle θ, measured above the
horizontal, that the hose should be directed so that the water
stream strikes the bottom of the wall at B. The speed of the
water at the nozzle is vc.

Ans:

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