Final exam:

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Final exam room 105 HECC, 8-10 am, Wednesday,
December 12th
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Kinematics
If
is given, you can find
and
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Kinematics of circular motion
If
is given, you can find
and
by integration,
similarly to linear motion
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General motion
y
x
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Dynamics I
Newtons First Law Second Law
Third Law
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A Recipe for Solving Problems

• Sketch
• Isolate the body (only external forces but
  not forces that one part of the object exert on
  another part)
• Identify all forces, maybe using 3rd law
• 2. Write down 2nd Newtons law

Choose a coordinate system Write 2nd Newtons
law in component form
You can use different coordinates for different
bodies, but be careful to relate them properly.
3. Solve for acceleration, then integrate
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Dynamics of rotational motion
For rigid bodies rotating about their axis of
symmetry
R
m2
Second Law
m1
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Kinetic energy of a rigid body or an ensemble of
particles
Applications rolling without slipping, combined
rotational and translational motion
Rotation of a rigid body about a fixed point O
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Conservation laws shortcuts to find velocities
bypassing Newtons law and accelerations

• Momentum
• Angular momentum
• energy

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Work Energy Theorem
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does NOT depend on path!
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Mechanical energy is conserved!
Know examples of conservative and
non-conservative forces If an unknown force
depends only on a coordinate, it is probably
conservative
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Conservation of Momentum
Sometimes only Fx or Fy may be equal to zero.
Then only px or py is conserved. If F is not
zero, but the collision is very short (F?t is
small as compared to change in momentum), you can
still use momentum conservation relating moments
of time immediately before and after the
collision.
If the collision is perfectly elastic, the
kinetic energy is conserved!
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Conservation of Angular Momentum
For symmetrical objects rotating about their axis
of symmetry
R
m2
Second Law
m1
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Harmonic Motion
Start from Newtons laws Derive an equation for
a small displacement from equilibrium When a
force or a torque is proportional to a
displacement from equilibrium, it smells like
harmonic motion
A and B from initial conditions