Boomerangs A Nexus mindmap http://www2.eng.cam.ac.uk/~hemh/boomerangs.htm 0 http://plus.maths.org/content/unspinning-boomerang?src=aop 1 References 0 unspinning-boomerang?src=aop 0 1 The answer is always B 0 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. 0 Why do they fly? 1 0 1 0 0 0 1 2 0 0 0 0 1 2 3 1 0 2 1 0 0 1 2 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. 3 0 1 3 2 2 General movement 2 0 0 0 0 Assume this form 2 1 1 fix angle theta 0 addition of both velocities, contribution of CM motion and rotational velocity 0 1 2 1 0 0 1 0 2 0 1 0 3 Force and Torque 3 0 0 0 0 1 0 0 0 1 0 2 2 Equations governing motion 4 Boomerangs