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Chapter 1: Q2DQ (page 293)

A diatomic molecule can be modeled as two point masses, m1and m2, slightly separated (Fig. Q9.2). If the molecule is oriented along the y-axis, it has kinetic energy K when it spins about the x-axis. What will its kinetic energy (in terms of K) be if it spins at the same angular speed about (a) the z-axis and (b) the y-axis?

Short Answer

Expert verified
  1. The kinetic energy is K.
  2. The kinetic energy is 0.

Step by step solution

01

Concept/Significance of Moment of inertia and rotational kinetic energy

The measure of rotational inertia of a body is equal to the moment of inertiaI of a body about a particular axis.

The expression for the rotational kinetic energy is given by,

K=12I蝇2

Here, is the moment of inertia, and蝇 is the angular velocity of body.

02

Determine the kinetic energy if it spins at the same angular speed about the z-axis(a)

Rotation about z-axis,

The kinetic energy of a diatomic molecule when it spins at the same angular speed about z-axis will be K. This is because the moment of inertial of the diatomic molecule about z-axis is equal to moment of inertial of the diatomic molecule about x-axis as angular speed is same.

Therefore, the required kinetic energy is K.

03

Determine the kinetic energy if it spins at the same angular speed about the y-axis(b)

Rotation about y-axis,

The kinetic energy of diatomic molecule when it spins at the same angular speed about y-axis will be zero. This is because the moment of inertia of a diatomic molecule about y-axis is zero, since the molecules are as point masses.

Therefore, the required kinetic energy is 0.

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