Two thin rods of length L are rotating with the same angualr speed w (in rad/s)

Question

Two thin rods of length L are rotating with the same angualr speed w (in rad/s) about axes that pass perpendiculalrly through one end. Rod A is massless but has a particle of mass 0.66kg attached to its free end. Rod B has a mass of 0.66kg, which is distributed uniformly along its length.

a_) Which rod ahas the great moment of interia? Explain.

b) Which rod has the greater rotational kinetic energy? Explain.

c) The length of each rod is 0.75m, and the angular speed is 4.2 rad/s. Find the kinetic energies of rod A withits attached particle and of rod B.

Explanation / Answer

a)

for rod A :

m = mass of the particle at the end = 0.66 kg

r = distance from the end = length of the rod = 0.75 m

moment of inertia = Ia = m r2 = 0.66 (0.75)2 = 0.37125

For rod B :

m = 0.66 kg

L = 0.75 m

moment of inertia = Ib = mL2/12 = (0.66) (0.75)2 /12 = 0.031 kgm2

so rod A has greater moment of inertia

b)

For A :

Rotational Kinetic energy = (0.5) I w2 = (0.5) (0.37125 ) (4.2)2 = 3.27 J

For B :

Rotational Kinetic energy = (0.5) I w2 = (0.5) (0.031) (4.2)2 = 0.27 J

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