Answer to Question #218255 in Mechanical Engineering for Sumeet Wagh

Question

Calculate the mass moment of inertia for the components and axes given below: a) A 3 kg rod which is 1.5m long about its centre b) A 2kg metal plate 300mmx400mm about an axis perpendicular to the plane of the plate through its centre. c) A 500g disc of diameter 100mm about an axis perpendicular to the plane of the plate through its centre. 

Answer 1

a.

$I= \frac{m}{12} * L\\ I= \frac{3}{12} * 1.5\\ I= 0.5625 kgm^2\\$

b.

$I_x= \frac{M}{12} *a^2\\ I_x= \frac{2}{12} *(300*300)\\ I_x= 15000000 gmm^2\\ I_y= \frac{M}{12} *b^2\\ I_y= \frac{2}{12} *(400*400)\\ I_y= 26666666.666667 gmm^2\\ I_z= \frac{1}{12}*M*(a^2+b^2)\\ I_z= \frac{1}{12}*2*(300^2+400^2) I_z=41666666.666667 gmm^2$

c.

$I_{y} = m * r²\\ I_{y} = 500 * 50²\\ I_{y} =0.0003125 kgm^2\\ I_{x} = m * r²\\ I_{x} = 500 * 50²\\ I_{x} =0.0003125 kgm^2\\ I_{z} = 0.5m * r²\\ I_{z} = 0.5*500 * 50²\\ I_{z} =0.000625 kgm^2\\$