Moment of inertia is a scalar. Therefore, if several objects are connected toget

Question

Moment of inertia is a scalar. Therefore, if several objects are connected together, the moment of inertia of this compound object is simply the scalar (algebraic) sum of the moments of inertia of each of the component objects. Use this principle to answer each of the following questions about the moment of inertia of compound objects:

A) A thin uniform 2.05 kg bar 1.40 m long has a small 1.15 kg mass glued to each end. What is the moment of inertia of this object about an axis perpendicular to the bar through its center?

B) What is the moment of inertia of the object in part A about an axis perpendicular to the bar at one end?

C) A 775 g metal wire is bent into the shape of a hoop 52.0 cm in diameter. Six wire spokes, each of mass 118 g, are added from the center of the hoop to the rim. What is the moment of inertia of this object about an axis perpendicular to it through its center?

Explanation / Answer

I (bar) = 1/12*M*L^2 = 1/12*2.50*1.40^2 = 0.408kg-m^2 I (mass) = m*r^2 = 1.45*0.70^2 = 0.7105kg-m^2 So total I = 0.408 + 2*0.7105 = 1.83 kg-m^2 2. For the bar the I is now 1/3*M*L^2 = 1/3*2.5*1.4^2 = 1.63kg-m^2 and 1 ball is m*r^2 = 1.45*1.4^2 = 2.84kg-m^2 (the othe is zero So I = 2.84+1.63 = 4.47kg-m^2 3. I'm assuming the masses are in grams So I of the wheel = m*r^2 = 0.775*0.30^2 = 0.0698kg-m^2 and each of the spokes is 1/3*m*l^2 = 1/3*0.113*0.30^2 = 3.39x10^-3kg-m^2 So I total = 0.0698 + 6*3.39x10^-3 = 0.0901kg-m^2

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