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Boomerangs
A Nexus mindmap
http://www2.eng.cam.ac.uk/~hemh/boomerangs.htm
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http://plus.maths.org/content/unspinning-boomerang?src=aop
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References
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unspinning-boomerang?src=aop
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The answer is always B
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1. What is (near enough) the shape of the flight path of a boomerang?
A.
out and back on a straight line;
B.
circular;
C.
around the four sides of a square.
2. If I swing a ball on string around my head it follows a circular path; in what direction does the force in the string act?
A.
downwards;
B.
always towards the centre of the circle;
C.
there is no force in the string.
3. An aeroplane wing works because:
A.
it is an anti-gravity device;
B.
when it moves through the air at high speed it generates lift;
C.
it flaps up and down.
4. A helicopter rotor has four blades each in the shape of:
A.
a feather;
B.
an airplane wing;
C.
a circular tube.
5. A cross-shaped boomerang resembles a helicopter rotor because:
A.
they both have four blades;
B.
they both generate lift when they spin;
C.
they work backwards as well as forwards.
6. The lift force of a spinning boomerang is directed mostly:
A.
downwards;
B.
towards the centre of its circular flight path;
C.
there is no lift force.
7. As a spinning boomerang moves forward the uppermost blade moves:
A.
at the same speed as the centre of the boomerang;
B.
faster than the centre of the boomerang because it is spinning and moving forwards at the same time;
C.
downwards.
8. The top of the boomerang generates more lift than the bottom because:
A.
it is bigger;
B.
it is moving faster;
C.
it is heavier.
9. The difference in lift between the top and the bottom of the boomerang:
A.
doesn't matter;
B.
forms a couple which causes gyroscopic precession;
C.
causes the boomerang to bend.
10. Lift on a boomerang causes circular motion and gyroscopic precession:
A.
which is too complicated for me to understand;
B.
which balance perfectly - truly a wonderful miracle of nature;
C.
which the Aborigines could have told you 10,000 years ago.
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Why do they fly?
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Let's assume that the boomerang is going to
go in a circle. We'll see if we can find a
consistent solution with this assumption.
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General movement
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Assume this form
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fix angle theta
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addition of both velocities,
contribution of CM motion
and rotational velocity
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Force and Torque
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Equations governing motion
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Boomerangs