Question

Explain how a child "pumps" on a swing to make it go higher? On the basis of the law of conservation angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate in order to keep the helicopter stable. A wheel is rotating freely about a vertical axis with a constant angular velocity. Small parts of the wheel come loose and fly off. How does this affect the rotational speed of the wheel? Is an pillar momentum conserved? Is kinetic energy conserved?

Answer 1

(a) The explanation is based on the third law of motion which says " To every action there is equal and opposite reaction". When the child  pushes his legs in front, there will be a recation force in backward direction .so the swing moves back . Similarly when the child pushes the legs backwards, the swing will move in forward direction.

(b) it is absolutley importan for a helocopter to have two rotors in order to conserve angular momentum.The main (top) rotor is the one that creates the lift. this top rotor is spinning in one direction all the time, so if there is nothing to counter this re-action then the helicopter would spin in the opposite direction to the top rotor. That's why the second rotor called as the tail rotor is used, this helps stop the counter rotation of the airframe and 'steers' the helicopter.

(c) according to law of conservation of angular momentum, initial angular momentum= final angular momentum

I1 w1 = I2 w2

when some parts of the wheel fly off, its moment of inertia I decreases and hence the rotational speed increases.that is because the angular momnetum is conserved.

the kinetic energy of the wheel is not conserved.