Three objects lie in the x,y plane. Each rotates about the z axiswith an angular

Question

Three objects lie in the x,y plane. Each rotates about the z axiswith an angular speed of 6.60 rad/s. The mass m of each object and its perpendicular distance r from the z axis are as follows: (1) m1 = 5.40 kg and r1 = 1.88 m, (2) m2 = 3.88 kg and r2 = 13.80 m, (3) m3 = 3.15 kg and r3 = 3.06 m. Find the tangential speed of each object. vT1 = m/s vT2 = m/s vT3 = m/s Determine the total kinetic energy of this system using the expression KE = 1/2 m1v1 2 + 1/2m2v2 2 + 1/2m3v3 2. J Obtain the moment of inertia of the system. kg. m2 Find the rotational kinetic energy of the system using the relation KER = 1/2 Iw2 to verify that the answer is the same as the answer to (b).

Explanation / Answer

a) Vt1 = w*R1 = 6.6 * 1.88 = 12.408 m/s

Vt2 = 6.6*13.8 = 91.08 m/s

Vt3 = 6.6*3.06 = 20.196 m/s

b) KE = 0.5[5.4* 12.408^2 + 3.88* 91.08^2 + 3.15*20.196^2] = 17.152 kJ

c) I = m1R1^2 + m2R2^2 + m3R3^2 = 5.4*1.88^2 + 3.88*13.8^2 + 3.15*3.06^2 =787.4883 kg-m^2

d) KE = 0.5*I*w^2 = 0.5*787.4883*6.6^2 = 17.152 kJ

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