Four small masses are connected by very light inflexible rods in the configurati

ID: 1457801 • Letter: F

Question

Four small masses are connected by very light inflexible rods in the configuration shown

below. The masses are: m1=m3= 2.00[kg] and, m2=m4= 3.00[kg]. The distances are: r1=r3=2.00[m] and, r2=r4= 4.00[m].

a. Find the moment of inertia of the system, if the axis of rotation is the x-axis (Figure a).

b. Find the moment of inertia of the system, if the axis of rotation is the z-axis (Figure b).

c. Calculate the kinetic energy of rotation of the system in cases (a) and (b), for a

constant angular velocity of 10.0 [rpm].

2 m1 m1 O-AiX.-O---*- m4 4

given,

m1=m3= 2.00[kg] and, m2=m4= 3.00[kg]

r1=r3=2.00[m] and, r2=r4= 4.00[m]

moment of inertia = mass * distance^2

moment of inertia is system is rotating about x axis = m2 * r2^2 + m4 * r4^2

moment of inertia is system is rotating about x axis = 3 * 4^2 + 3 * 4^2

moment of inertia is system is rotating about x axis = 96 kg.m^2

moment of inertia is system is rotating about z axis = m2 * r2^2 + m4 * r4^2 + m1 * r1^2 + m3 * r3^2

moment of inertia is system is rotating about z axis = 3 * 4^2 + 3 * 4^2 + 2 * 2^2 + 2 * 2^2

moment of inertia is system is rotating about z axis = 112 kg.m^2

kinetic energy = 0.5 * moment of inertia * w^2

for figure a)

w = 10 rpm or 1.0472 rad/sec

kinetic energy = 0.5 * 96 * 1.0472^2

kinetic energy = 52.638 J

for figure b)

kinetic energy = 0.5 * 112 * 1.0472^2

kinetic energy = 61.411 J

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