Calculating Moment of Inertia for Square Particle System

AI Thread Summary
To calculate the moment of inertia for a system of four 30g masses at the vertices of a square with 90cm sides, the formula I = mr² is applied. Each mass is located at a distance of 45cm from the center, determined as the hypotenuse of a right triangle formed by half the square's sides. The moment of inertia is then calculated by multiplying the individual contributions of each mass by four. This approach is confirmed to be correct for the given configuration. The solution effectively demonstrates the application of the moment of inertia formula in a square particle system.
duplaimp
Messages
33
Reaction score
0

Homework Statement


There are four masses (particles) with a mass of 30gr each and they are at the vertices of a square that has each side with a length of 90cm.
What is the moment of inertia of this system through a perpendicular axis that is at the center of the square?

The Attempt at a Solution


My idea is to use the moment of inertia I = mr^{2} (Point mass m at a distance r from the axis of rotation.)
Then the distance will be the hypotenuse of a right triangle that has each side with 45cm and putting that into the moment of inertia and multiply by 4

Is this correct?
 
Physics news on Phys.org
Yes, that is correct.
 
  • Like
Likes 1 person
Thank you
 
I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
Thread 'A cylinder connected to a hanging mass'
Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...

Similar threads

Back
Top