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WhoThat3
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Hey so I got stuck on this question and was wondering if I can get some help. I got up to part c, but I am not sure about it. Also for part a I am not sure if I used the right equations for Inertia. Here it is.
An object in the shape of a square with a circle cut in the center of it spins about its center of mass. The axis of rotation is perpendicular to the plane of the square. The object has mass M and has edges of length 2R. ITs density is constant.
Picture:
A Square with an inscribed circle of radius R both with the same center.
a) Ms = mass of whole squaer; Mc = mass of circle that was cut out.
Express Moment of Inertia in terms of Ms, Mc, and R.
b)How does the object's mass relate to the masses Ms and Mc?(Equation)
c) What is the ratio of Ms to Mc? *****
d) Use answer from part b and c to express Ms and Mc each in terms of M.
e) Express Moment of Inertia in terms of M and R.
I = 1/2*MR^2
I=1/12*M(L^2 + W^2)
a) Icircle=1/2*MR^2
Isquare=1/12*M((2R)^2+(2R)^2)
Itogether=Isquare-Icircle
I=2/3*MsR^2-1/2*McR^2
I=R^2*(2/3*Ms-1/2*Mc) -- answer for part A
b) M=Msquare-Mcircle
c) Ok here is my probelm, I never was good with ratios, but I did try to find their areas; Asquare = 4R^2 and Acircle = R^2*pi and if I made those in a ratio I get a 4:pi ratio, which is close to 4:3 which does seem reasonable. But I just want to double check. I have not gone on since the other parts fo this question depend on this one. Thanks again
Homework Statement
An object in the shape of a square with a circle cut in the center of it spins about its center of mass. The axis of rotation is perpendicular to the plane of the square. The object has mass M and has edges of length 2R. ITs density is constant.
Picture:
A Square with an inscribed circle of radius R both with the same center.
a) Ms = mass of whole squaer; Mc = mass of circle that was cut out.
Express Moment of Inertia in terms of Ms, Mc, and R.
b)How does the object's mass relate to the masses Ms and Mc?(Equation)
c) What is the ratio of Ms to Mc? *****
d) Use answer from part b and c to express Ms and Mc each in terms of M.
e) Express Moment of Inertia in terms of M and R.
Homework Equations
I = 1/2*MR^2
I=1/12*M(L^2 + W^2)
The Attempt at a Solution
a) Icircle=1/2*MR^2
Isquare=1/12*M((2R)^2+(2R)^2)
Itogether=Isquare-Icircle
I=2/3*MsR^2-1/2*McR^2
I=R^2*(2/3*Ms-1/2*Mc) -- answer for part A
b) M=Msquare-Mcircle
c) Ok here is my probelm, I never was good with ratios, but I did try to find their areas; Asquare = 4R^2 and Acircle = R^2*pi and if I made those in a ratio I get a 4:pi ratio, which is close to 4:3 which does seem reasonable. But I just want to double check. I have not gone on since the other parts fo this question depend on this one. Thanks again