Interconnected rigid bodies
Interconnected rigid bodies:
If two bodies are interconnected, there combined free body diagram can be made. If is the net external force on the bodies
If is the net moment on the bodies about point O, then
Conservation of momentum
Thus, if the net external force on the body is zero, its linear momentum remains conserved.
Similarly, if resultant moment about a point is zero, the angular momentum about O remains conserved.
In this case the angular momentum about G remains constant.
Example 1: In turbine, a jet of water is made to impinge on the vanes of turbine and get deflected by a certain angle. During this process, a force is exerted by the jet on the vane and that causes rotation of the turbine. The force exerted by the jet on the vane can be determined by applying momentum equations. This is illustrated.
Consider that the turbine is stationary and Q m3/sec water falls on it. The mass of water whose momentum is changed in 1 sec is
Applying impulse momentum equation
The water exerts equal and opposite force on the blade.
There is no net vertical force in this problem. This is because of symmetry.