The figure below shows a side view of a car tire and itsradial dimensions. The o

Question

The figure below shows a side view of a car tire and itsradial dimensions. The outer radius of the tire is 33.0 cm, and theinner radius is 16.5 cm. The rubber tire has two sidewalls ofuniform thickness 0.580 cm and a treadwall of uniform thickness 2.50 cm and width 19.5 cm. Assume the rubber has a uniform densityequal to 1.10 x 103 kg/m3.Find its moment of inertia about an axis through its centerperpendicular to the plane of the sidewalls. Figure(http://www.webassign.net/pse/p10-29.gif)
kg·m2 The figure below shows a side view of a car tire and itsradial dimensions. The outer radius of the tire is 33.0 cm, and theinner radius is 16.5 cm. The rubber tire has two sidewalls ofuniform thickness 0.580 cm and a treadwall of uniform thickness 2.50 cm and width 19.5 cm. Assume the rubber has a uniform densityequal to 1.10 x 103 kg/m3.Find its moment of inertia about an axis through its centerperpendicular to the plane of the sidewalls. Figure(http://www.webassign.net/pse/p10-29.gif)
kg·m2

Explanation / Answer

   let us take the tire as consisting of threeparts
   the two side walls are each treated as hallowcylinder of inner radius 16.5 cm, outer radius 30.5 cm and height0.580cm
   the tead region is treated as hollow cylinder ofinner radius 30.5 cm, outer radius 33.5 cm and height 19.5cm
   the moment of inertia is given by
   I = (1 / 2) m (R12 +R22) for the hollow cylinder
   for the side wall we get
   m = [(0.305 m)2 - (0.165m)2] (5.80 x 10-3 m) (1.10 x 103kg / m3)
      = .......... kg
   Iside = (1 / 2) (11.0 kg) [(0.330m)2 - (0.305 m)2]
           =......... kg . m2
   for the entire tire we get that
   Itoatl = 2 Iside +Itread
           =......... kg . m2

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