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 3.90 rad/s. Find the moment of inertia about the x axis kg * m^2 Find the total rotational kinetic energy evaluated from 1/2 I omega_2. J Find the tangential speed of each particle. 4.00 kg particle m/s 2.00 kg particle m/s 3.00 kg particle m/s Find the total kinetic energy evaluated from sigma 1/2 m_iv_i^2. J Compare the answers for kinetic energy in parts (b) and (d).

Explanation / Answer

m1 =4 kg , y1 =3 m

m2 = 2kg, y2 = -2 m

m3 =3 kg , y3 =-4 m

w =3.9 rad/s

(a) Ix = m1y1^2+m2y2^2 +m3y3^2

Ix = (4*3*3) +(2*2*2)+(3*4*4)

Ix = 92 kg.m^2

(b) K.Er = (1/2)Iw^2 = (1/2)(92*3.9*3.9)

Rotational kinetic energy K.Er = 699.66 J

(c) v =rw

v1 =y1*w = 3*3.9 = 11.7 m/s

v2 = 2*3.9 = 7.8 m/s

v3=4*3.9 = 15.6 m/s

(d) K.E= (1/1)m1v1^2+(1/2)m2v2^2+(1/2)m3v3^2

K.E = (0.5*4*11.7*11.7)+(0.5*2*7.8*7.8)+(0.5*3*15.6*15.6)

K.E = 699.66 J

(e) Rotational kinetic energy = Total kinetic energy

Total kinetic energy is sum of translational kinetic energy and rotationla kinetic energy

But there is no translatory motion.

So the Total kinetic energy is equal to rotational kinetic energy

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