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Today
Today
’
’
s Lecture
s Lecture
Lecture 16:
Course Review;
Kinematics,
Newton’s Laws of Motion,
Conservation of Energy
Chapter 11, Rockets

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*Sign up* Review
Review
Kinematics
Kinematics

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*Sign up* Circular Motion and Acceleration
Circular Motion and Acceleration
Consider the two unit vectors that
are convenient for angular motion:
r
cos
i
sin
j
−
sin
i
cos
j
The position vector can now be written
r
r
r
r
cos
i
sin
j
x
i
y
j
The velocity vector is simply the time derivative of the position vector.
For circular motion the radius of curvature,
r
, is constant. However,
f = f(
t
),
is time dependent. This means to find the velocity vector we must
be careful when taking the derivative of the position vector – chain rule!

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*Sign up* Circular Motion and Acceleration
Circular Motion and Acceleration
Consider the two unit vectors that
are convenient for angular motion:
r
cos
i
sin
j
−
sin
i
cos
j
The velocity vector can now be expressed:
Taking the derivative of the velocity
yields the acceleration. Assuming a
constant rate of rotation,
w
:
The radial acceleration points
radially
inward
! What
happens when there is angular
acceleration? Stay tuned!
v
d
r
dt
r
d
cos
dt
i
d
sin
dt
j
v
r
−
sin
i
cos
j
d
dt
r
v
a
d
v
dt
r
−
d
sin
dt
i
d
cos
dt
j
a
−
r
cos
i
sin
j
d
dt
−
2
r
r
−
v
2
r
r

Review
Review
Dynamics
Dynamics

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*Sign up* Newton
Newton
’
’
s Second Law
s Second Law
is the net force
This is the vector sum of all the forces acting on the

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