igid rods of negligible mass lying along the y axis connect three particles. The
ID: 1395540 • Letter: I
Question
igid rods of negligible mass lying along the y axis connect three particles. The system rotates about the x axis with an angular speed of 1.50 rad/s.
(a) Find the moment of inertia about the x axis.
kg · m2
(b) Find the total rotational kinetic energy evaluated from 1/2Iw^2
J
(c) Find the tangential speed of each particle.
(d) Find the total kinetic energy evaluated from
.
J
(e) Compare the answers for kinetic energy in parts (b) and (d).
Explanation / Answer
a)
m1 = 4 kg , r1 = 3 m
m2 = 2 kg , r2 = 2 m
m3 = 3 kg , r3 = 4 m
Moment of inertia of system , I = m1 r12 + m2 r22 + m3 r32 = 4 (3)2 + 2 (2)2 + 3 (4)2 = 92 kgm2
b)
w = 1.50 rad/s
Rotational KE , = (0.5) I W2 = (0.5) (92) (1.50)2 = 103.5 J
c)
V1 = r1 w = 3 x 1.5 = 4.5 m/s
V2 = r2 w = 2 x 1.5 = 3 m/s
V3 = r3 w = 4 x 1.5 = 6 m/s
d)
Total kinetic energy is given as ::
KE = (0.5) m1 v12 + (0.5) m2 v22 + (0.5) m3 V32
KE = (0.5) (4) (4.5)2 + (0.5) (2) (3)2 + (0.5) (3) (6)2 = 103.5 J
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