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 1.50 rad/s.

(a) Find the moment of inertia about the x axis.
                               kg · m2

(b) Find the total rotational kinetic energy evaluated from 1/2 Iw^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) I = 4kg * (3m)² + 2kg * (2m)² + 3kg * (4m)² = 92 kg·m²

b) Ek = ½ * 92kg·m² * (1.5rad/s)² = 103.5 J

c) v = r. From top down:
v = 1.5 rad/s * 3m = 4.5 m/s
v = 1.5 rad/s * 2m = 3.0 m/s
v = 1.5 rad/s * 4m = 6.0 m/s

d) Ek = ½(4kg * (4.5 m/s)² + 2kg * (3.0 m/s)² + 3kg * (6.0 m/s)²) = 103.5 J

e) from (b) and (d) kinetic energies are equal.

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