rotational dynamics **3 that the particle\'s radlal given by the vector equation

Question

rotational dynamics **3

that the particle's radlal given by the vector equation ar- × ( × r). 145 Three particles are located along the X-axis as follows: 3.0 kg atz- -5.0 m, 10.0kgata 5.0m, and 4.0 kgata -2.0m. For this system, what is (a) the coordinate of the center of mass, (b) the moment inertia with respect to the Y-axis, (e) the radius of gyration (defined i Example 1) with respect to the Y-axis, (d) the moment of inertia wit! respect to an axis perpendicular to the X-axis and passing throug

Explanation / Answer

m1 = 3 kg    , x1 = -5 m

m2 = 10 kg    , x2 = 5 m

m3 = 4 kg    , x3 = 2 m

a)

center of mass is given as

X = (m1 x1 + m2 x2 + m3 x3) / (m1 + m2 + m3)

X = (3(-5) + 10(5) + (4)(2)) / (3 + 10 + 4)

X = 2.53 m

b)

moment of inertia is given as

I = m1 x12 + m2 x22 + m3 x32

I = 3 (-5)2 + 10 (5)2 + 4 (2)2

I = 341 kgm2

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