Three objects lie in the x , y plane. Each rotates about the z axis with an angu
ID: 1546340 • Letter: T
Question
Three objects lie in the x, y plane. Each rotates about the z axis with an angular speed of 6.18 rad/s. The mass m of each object and its perpendicular distance r from the z axis are as follows: (1) m1 = 5.94 kg and r1 = 1.84 m, (2) m2 = 3.76 kg and r2 = 14.90 m, (3) m3 = 2.85 kg and r3 = 2.94 m.
(a) Find the tangential speed of each object.
(b) Determine the total kinetic energy of this system using the expression KE = ½m1v12 + ½m2v22 + ½m3v32.
J
(c) Obtain the moment of inertia of the system.
kg · m2
(d) Find the rotational kinetic energy of the system using the relation KER = ½I2 to verify that the answer is the same as the answer to (b).
J
Explanation / Answer
(a) vTi = i * ri
so
vT1 = 6.18rad/s * 1.84m = 11.37 m/s
vT2 = 6.18rad/s * 14.9m = 92.08 m/s
vT3 = 6.18rad/s * 2.94m = 18.16 m/s
(b)
KE = ½*[5.94kg*(11.37m/s)² + 3.76kg*(92.08m/s)² + 2.85kg*(18.16m/s)²]
KE = 97859 J
(c) I = mi * ri² = [5.94*1.84² + 3.76*14.90² + 2.85*2.94²] kg·m² = 862.99 kg·m²
(d) KE = ½I² = ½ * 862.9kg·m² * (6.18rad/s)² = 16478.110 J
to three significant digits.
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