Kator01: how much different is the (5 kg and 2 kg, 100 cm) rod from a tennis racket tossed by MIT? 

https://www.youtube.com/watch?v=DY3LYQv22qY

The motion of the racket is probably started in a near straight line or long arc. Then the handle is pushed so that the linear momentum of the racket is pushed into a spin. This is very similar to what the pin does to the 5 kg and 2 kg rod. 

The tennis racket does not find the center of kinetic energy. It could; the racket is free to do what it likes. But instead, the spinning racket finds the center of mass. And the center of mass, for a spinning object, is the center of linear (arc) momentum.

Your 58 cm radius (for the 5 kg and 2 kg rod) indicates that the center of energy and the center of mass are not in the same place, which is true. But experiments find the 'center of mass' and the energy does not remain the same. 

I get 59.16 cm radius for center of energy, and of course 50 cm (from the 5 kg end) for the center of mass. But you can't have it both ways; one of these centers is wrong.   

A one kilogram mass moving 24.26 m/sec will rise 30 meters. This is 24.26 units of linear momentum. 

An evenly spaced stack of 30 one kilogram masses, that is 30 m high, can be used to accelerate a 170 kg rim. After the stack has dropped one meter the entire system is moving 1.7155 m/sec for 343.1 units of linear momentum.

As demonstrated by the cylinder and sphere; a spinning rim can transfer all of its motion to a small mass.

A one kilogram mass moving 343.1 m/sec can rise 6000 meters. It need only rise 30.

sorry for the late answer, now, your 20.5 m is right...silly error in my calculation.

your quote "As demonstrated by the cylinder and sphere; a spinning rim can transfer all of its motion to a small mass."

Exactly and this is why with every example givenh ere by you I first look at the big-mas to small-mass momentum-transfer

In the case of your last example ( 5 kg at 30 cm-2 kg at the bottom of the rod) this is not the case. Simply the moment of inertia
is changed.

Mike



Mike

Yes: moment of inertia changes big time. From 'roughly' 1 kg * 20.5 m * 20.5 m to 1 kg *.5 m * .5 m; from 420.25 to .25. Do numbers have no meaning? What indicates that these numbers are justifiable?

Can the 1 kg moving 1 m/sec on the end of the 20.5 meters string rise higher that a one kg mass moving 1 m/sec on the end of a .5 m string?

Can the 420.25 share more momentum with a second object?

Can the 420.25 crush more stone? Lift more water? Chop more wood?

The moment of inertia for a point mass is mr².

Angular momentum is: moment of inertia (mr²) times angular velocity 'omega' (which is linear speed around the arc / radius).

m * r * r  *v (linear) / r =  angular momentum (L)          r/r is 1

So  L = m * v (linear) * r

The angular momentum for the 20.5 meter pendulum is about;  L =  2 kg * 1.0244 m/sec *21 m + (5 kg *  20 .3 m * .9902 m/sec) = 43.02 + 100.50 = 143.52

The angular momentum for the .5 meter pendulum is about;  L =  2 kg * 2 m/sec * 1 m + (5 kg *  .3 m * .6m/sec) = 4 + .9 = 4.9

Why is 143.52 so much higher? Can it chop more wood? Crush more stone? Rise higher? Share more momentum? No they are absolutely the same thing: 1 kg moving 1 m/sec.

mr² is simply wrong.

new martial arts techniques: jumping kicks


watch his increased rotation-speed when he draws both arms tight to his body


https://www.youtube.com/shorts/gXm-ww3nNYE


it looks unreal


Mike


PS: bear with me..still  suffer nasty cough..cant concentrate to follow your last post