# Mass Moment of Inertia and Translational Motion

1. Calculate the mass moment of inertia about the x axis. The total mass of the object is 13 kg.

2. The plate with two holes is made of steel with a density of 7800 kg-m3. The radius of each hole is 5 cm. Determine its mass moment of inertia about the z-axis.

3. Determine the mass moment of inertia about the y axis. The thin plate has a mass of 0.1 slug and thickness of 0.05 in.

4. A 50 lb door is supported as shown in the figure on 2 rollers A and B resting on a horizontal track. A constant force P = 10 lb is applied. What will be the velocity of the door 5 secs after starting from rest?

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#### Solution Preview

1.)

Dimensions of the cuboid : b = 3 cm, h = 5 cm, t = 4 cm

Dimensions of the triangular block : l = 6 cm, h = 5 cm, t = 2 cm.

volume of the cuboid Vc = 4*5*3 = 60 cm^3

volume tof triangle Vt = (1/2)*6*5*2 = 30 cm^3

Total volume V = Vt + Vc = 90 cm^3

Total mass m = 13 kg

density d = m/V = 13/90 kg/cm^3

mass of the cuboid mc = Vc*d = 60*13/90 = 26/3 kg

mass of the triangle mt = Vt*d = 30*13/90 = 13/3 kg

moment of inertia of the cuboid w r to x axis,

Icx = (1/3)*mc*(h^2 + b^2) = (1/3)*(26/3)*(5^2 + 3^2) = 98.22 kg.cm^2

Position of the C.M. of the triangular block with respect to x-axis : (y= 3 + 6/3, z=5/3) = (5, 5/3)

=> r = sqrt(25 + 25/9) = (5/3)*sqrt(10) cm

=> r^2 = 250/9 cm^2

moment of inertia of ...

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