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Four point masses of 3.0 kg each are arranged in square on massless rods. The length of a side of the square is 0.50 m. what is the rotational inertia about an axis.
a) passing through masses B and C?
A______B
| the sides are 0.50m
D______C
b) Passing through masses A and C? Diaganal
A_____B
| |
D_____C
c) passing through the center of the square and perpendicular to the plane of the square?
A------B
| . |
| | side is .50m
D------C there is a spot in the middle of the square

Show me how you find the answere step by step
I have a lot of problems like this one so I need to know how you find the answer thanks

2007-01-09 14:18:56 · 1 answers · asked by collegegirl 2 in Science & Mathematics Physics

1 answers

These types of problems require looking at the masses with respect to the way you would like to rotate them on the axis you are evaluating. A point mass is defined as a mass without dimension. That means that for an axis that passes through the mass, there is no inertia about the axis for that mass. Also the rods are declared mass less so they do not contribute.

I=m*r^2

Step by step:
a) B and C are on the axis, so they have no inertia with respect to that axis. D and C are each .5 m away attached by rods.

So I=D*.5^2+C*.5^2

b) For A nd C, they do not contribute. B and D are each
.5*sqrt(2)/2 away from the axis and connected through the rods.

I=B*(.5*sqrt(2)/2)^2 +D*(.5*sqrt(2)/2)^2

c) could be a trick question since there is no mechanical connection between the point masses and the center of the square. I will assume there is a mass less plane that makes the connection. In this case all four masses contribute as they are a distance of .5*sqrt(2)/2 from the center
I=A*(.5*sqrt(2)/2)^2 +B*(.5*sqrt(2)/2)^2 +
+C*(.5*sqrt(2)/2)^2 +D*(.5*sqrt(2)/2)^2

J

2007-01-11 03:38:51 · answer #1 · answered by odu83 7 · 1 0

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