Kinetic rotational energy problem

Remember to always check your work and make sure it aligns with the given equations and information, and to also think critically about the concepts being discussed. Keep up the good work!In summary, the kinetic energy of a diatomic molecule spinning about the x-axis is K. When spinning at the same angular speed about the z-axis, the kinetic energy remains K. However, when spinning about the y-axis, the kinetic energy becomes 0 due to the perpendicular distance between the atoms and the rotation axis being 0. It is important to always check and critically think about solutions to ensure accuracy.
  • #1
spaghetti3451
1,344
33

Homework Statement



A diatomic molecule can be modeled as two point masses, m1 and m2, slightly separated. 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
(b) the y-axis?

Homework Equations



K = 0.5Iω2

The Attempt at a Solution



(a) I stays the same as the atoms are the same perpendicular distance from the origin. So the kinetic energy = K.

(b) I = 0 as the perpendicular distance between each atom and the rotation axis (the y-axis) is 0. So, kinetic energy = 0.

It would help me if you comment on my solution.
 
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  • #2
Looks good to me.
Was there anything in particular you were concerned about?
 
  • #3
Oh no, just wanted to know if my answers were good. Thanks, by the way!
 
  • #4
No worries.
Looks like you need to develop ways to decide for yourself if your answers are good.
 
  • #5


Your solution is correct. When the molecule is rotating about the z-axis, the moment of inertia stays the same as the atoms are at the same perpendicular distance from the axis. Therefore, the kinetic energy will be the same as when it is rotating about the x-axis.

However, when the molecule is rotating about the y-axis, the moment of inertia becomes 0 as the perpendicular distance between each atom and the axis is 0. This means that there is no rotational energy and the kinetic energy will also be 0.

It is important to note that the kinetic energy in this problem is solely due to rotational motion. If the molecule was also translating, there would be an additional contribution to the kinetic energy.
 

1. What is kinetic rotational energy?

Kinetic rotational energy is the energy that an object possesses due to its rotation. It is calculated as half of the moment of inertia of the object multiplied by the square of its angular velocity.

2. How is kinetic rotational energy different from kinetic energy?

Kinetic rotational energy is a type of kinetic energy that is specific to rotating objects, while kinetic energy is the energy an object possesses due to its motion. Both types of energy are measured in joules.

3. How is kinetic rotational energy important in physics?

Kinetic rotational energy plays a crucial role in understanding the motion and behavior of rotating objects, such as wheels, gears, and celestial bodies. It is used in various equations and formulas to calculate the motion and dynamics of these objects.

4. Can kinetic rotational energy be converted into other forms of energy?

Yes, according to the law of conservation of energy, kinetic rotational energy can be converted into other forms of energy, such as potential energy or heat energy. For example, when a spinning top falls, its rotational energy is converted into potential energy and then into kinetic energy as it moves downwards.

5. How can we calculate the kinetic rotational energy of an object?

The kinetic rotational energy of an object can be calculated by using the formula E = 1/2Iω^2, where E is the kinetic rotational energy, I is the moment of inertia, and ω is the angular velocity of the object. The moment of inertia can be calculated by considering the mass and distribution of mass of the object.

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