Rigid rods of negligible mass lying along the y axis connect three particles. Th

Question

Rigid rods of negligible mass lying along the y axis connect three particles. The system rotates about the x axis with an angular speed of 1.00 rad/s.

(a) Find the moment of inertia about the x axis._____ kg x m^2

(b) Find the total rotational kinetic energy evaluated from 1/2 Iw^2______ J

(c) Find the tangential speed of each particle

  (e) Compare the answers for kinetic energy in parts (b) and (d).   

4.00 kg particle________ m/s 2.00 kg particle______m/s 3.00 kg particle______ m/s

(d) Find the total kinetic energy evaluated from 1 2 mivi2 __________ J

  (e) Compare the answers for kinetic energy in parts (b) and (d).   

Explanation / Answer

(a)

the moment of inertia, I = mr^2
the total moment of inertia ,

   I = I1+I2+I3

     = 4*9+2*4+3*16   (since I = mr^2 )

     = 92 kg-m^2

(b)

the total rotational kinetic energy,

E = 1/2I?^2

     = 46 J

(c)

  the tangential speed of each particle,

V = r?

V1 = 3*1.0

        = 3 m/s

V2 = 2 m/s

V3 = 4 m/s

(d)

the total kinetic energy,

E = E1+E2+E3

   = 46 J

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