Question

A 1.0 kg mass is located at the origin of the (?, ?) plane, another 1.0 kg mass is located at the point (0.12, 0), and a 2.0 kg mass is located at the point (0.06, 0.08), where the (?, ?) coordinates are given in meters. The three masses are fixed relative to each other by massless rods.

a) Find the moment of inertia of this object about an object perpendicular to the (?, ?) plane & passing through the 2.0 kg mass.

b) Use the parallel axis theorem to find the moment of inertia about an axis passing through the center of mass & perpendicular to the (?, ?) plane.

c) Find the moment of inertia about an axis that passes through both of the 1.0 kg masses

d) Find the coordinates of the center of mass of this triangular object.

Answer 1

(a) Va06)2+ (o.08) AC = (0.06,0.09) 2g O.I m C Ikg BC Y(o.06)2+ Co.08) Ikg (90) 2. Cos,o) B A MI 0.02 kgm We nead to find the centun of mass now, (take A as ovigin) mz2tm3 Xcm lx o-12 t 2x0-06 lxo + Xm o-061m. mitm2+ms = xo +1xO + 2xD-08 o.04 em 4- (m yem)=o.06, 0.04) center of maas = From the Ponallel axis theoyem, Iem +md I I- md2 Icm We know, I = 0-02. Kgm2 m=1+1+2= 4 Ka. ddistance behween the two porallel 0.08-0.04 = o.04 m. Mass T = MI about center of 4o.04) D.02 T = Cn o.o136 kgm2

about axis passing though A MI CC) 2 x Co-12 [* 2メ AC- + 1メAE1 xCo-12) o.o2 - o.o144 o 0344 Kam2 MI about axis Pasing thaough B, lx (o-12) 2x Co.1) o.o344 kam centre of of the found in Solution for pant (b) aluady riangular ofject has been mass (d)