The masses and coordinates of four particles are indicated in the following tabl
ID: 2177922 • Letter: T
Question
The masses and coordinates of four particles are indicated in the following table. 25 g x = 2.0 cm y = -4.0 cm 40 g x = -2.0 cm y = -2.0 cm 50 g x = 3.0 cm y = 3.0 cm 45 g x = 1.0 cm y = 2.0 cm (a) What is the rotational inertia of this collection about the x axis?(b) What is the rotational inertia of this collection about the y axis?
(c) What is the rotational inertia of this collection about the z axis?
(d) Suppose the answers to (a) and (b) are A and B, respectively. Then what is the answer to (c) in terms of A and B? A - B AB A + B (A + B)2 The masses and coordinates of four particles are indicated in the following table. 25 g x = 2.0 cm y = -4.0 cm 40 g x = -2.0 cm y = -2.0 cm 50 g x = 3.0 cm y = 3.0 cm 45 g x = 1.0 cm y = 2.0 cm (a) What is the rotational inertia of this collection about the x axis?
(b) What is the rotational inertia of this collection about the y axis?
(c) What is the rotational inertia of this collection about the z axis?
(d) Suppose the answers to (a) and (b) are A and B, respectively. Then what is the answer to (c) in terms of A and B? A - B AB A + B (A + B)2 25 g x = 2.0 cm y = -4.0 cm 40 g x = -2.0 cm y = -2.0 cm 50 g x = 3.0 cm y = 3.0 cm 45 g x = 1.0 cm y = 2.0 cm (a) What is the rotational inertia of this collection about the x axis?
(b) What is the rotational inertia of this collection about the y axis?
(c) What is the rotational inertia of this collection about the z axis?
(d) Suppose the answers to (a) and (b) are A and B, respectively. Then what is the answer to (c) in terms of A and B? A - B AB A + B (A + B)2 A - B AB A + B (A + B)2 25 g x = 2.0 cm y = -4.0 cm 40 g x = -2.0 cm y = -2.0 cm 50 g x = 3.0 cm y = 3.0 cm 45 g x = 1.0 cm y = 2.0 cm
Explanation / Answer
a) Ix = 25 x42 + 40 x 22 + 50 x 32 + 45 x 22 = A
b) Iy = 25 x 22 + 40 x 22 + 50 x 32 + 45 x 12 = B
c) Iz = 25 x (42 + 22 ) + 40 x (22 + 22 ) + 50 x( 32 + 32 ) + 45 x (22 + 12 )
Iz = A + B
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