(a) Explanation Given information: The mass of tetrahedron is m . Calculation : Sketch the tetrahedron series of vertical slices as shown in Figure 1. First divide the tetrahedron into a series of thin vertical slices of thickness d z as shown below: x = − a c z + a = a ( 1 − z c ) y = − b c z + b = b ( 1 − z c ) Find the mass d m of the slab as shown below: d m = ρ d V = ρ ( 1 2 x y d z ) = 1 2 ρ a b ( z c ) 2 d z Integrate the m as shown below: m = ∫ d m = ∫ 0 c 1 2 ρ a b ( 1 − z c ) 2 d z = 1 2 ρ a b [ − c 3 ( 1 − z c ) 3 ] 0 c = 1 2 ρ a b [ − c 3 ( 1 − c c ) 3 ] m = 1 6 ρ a b c Find the direct integration the mass product of inertia I z x by using the formula as shown below: d I z x = d I z ′ x ′ + z E L x E L d m (b) To determine Deduce I y z and I x y from the result obtained in part a .

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Inertia can be termed as a resistance offered by a body to change its state. A rigid body initially at rest will apply resistance when acted by an external force that tends to change its state of rest or velocity, or a body initially at motion will provi…

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Chapter 9.6, Problem 9.162P

(a)

To determine

Find the mass product of inertia Izx by direct integration.

(b)

To determine

Deduce Iyz and Ixy from the result obtained in part a.

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Chapter 9.6, Problem 9.161P

Chapter 9.6, Problem 9.163P

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Find the mass product of inertia I z x by direct integration.

Solution Summary: The author explains how to find the mass product of inertia I_zx by direct integration.