Unit 6: Quiz 7a
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Consider the diatomic molecule oxygen, O2, which is rotating in
the xy plane about the z-axis passing through its center,
perpendicular to its length. The mass of each oxygen atom is
2.66 x 10-26 kg, and at room temperature, the average
separation between the two oxygen atoms is d = 1.21 x 10-10 m.
a) Calculate the moment of inertia of the molecule about the z-axis.
b) If the angular velocity of the molecule about the z-axis is 4.6 x 1012
rad/s, what is the rotational Kinetic Energy?
Consider the diatomic molecule oxygen, O2, which is rotating in
the xy plane about the z-axis passing through its center,
perpendicular to its length. The mass of each oxygen atom is
2.66 x 10-26 kg, and at room temperature, the average
separation between the two oxygen atoms is d = 1.21 x 10-10 m.
a) Calculate the moment of inertia of the molecule about the z-axis.
I = Smr 2
I t = 2(mr 2 )
I t = 2(2.66x10 -26 kg)(6.05x10 -11 m / s)2 = 1.95x10 -46 kg × m 2
b) If the angular velocity of the molecule about the z-axis is 4.6 x 1012
rad/s, what is the rotational Kinetic Energy?
1
I tw 2
2
1
Ek = (1.95x10 -46 kg × m 2 )(4.6 x 1012 )2 = 2.06x10 -21 J
2
Ek =