Masses are connected by cables. The masses are so tiny that their radii can be i
ID: 1990015 • Letter: M
Question
Masses are connected by cables. The masses are so tiny that their radii can be ignored, but they each do have mass. The cables have no mass and are super rigid.
They are arranged like this
* * *
* * *
* * *
The straight distance between any two masses is d.
A pivot is placed through the bottom left mass.
* * *
* * *
P * *
The entire object is released. It swings around the pivot. When the object is as low as it can go, what is its rotational velocity?
What I tried with this one I used KErot = mgh, but I don't know what the max height would be =.
Also, the moment of inertia for the whole thing would be 3*M*D^2+6*M*D^2 right?
Explanation / Answer
we can do it with the help of centre of mass
initially cm of mass will be
* * *
* c *
p * * here c is cm the distance of cm from pivot is 2 d
after rotation situation is like
p
c center of mass will be just below pivot at distance of2 d so that there is no net torque on system.
hence now we can solve for cm as single mass of mass 6m.
KErot = 6mgh
here h will be the distance moved by cm which id d+2 d
and moment of inertia will be 6m*(2 d)2 as cm is 2 d from pivot.