Loss of rotational energy to thermal energy

• esalbred
In summary, the conversation discusses calculating the loss of energy to thermal energy after a lump of clay is dropped onto a frictionless turntable at a certain speed. The approach involves using the formulas for rotational kinetic energy and comparing the initial and final kinetic energies. The difference between the two is the energy converted to heat. The conversation also mentions the concept of completely inelastic collisions and how they result in a lot of energy being converted to heat. Ultimately, the conversation provides helpful hints in the right direction for solving the problem.
esalbred
I've got a turntable whose bearing is frictionless rotating at a certain speed. A mass of clay is dropped on to it and sticks a certain distance from the center. I've been able to calculate the new angular speed of the turntable after the lump falls on it, but the follow up question is to calculate the loss of energy to thermal energy.

The bearing is frictionless, so my hunch is it has to do with the torque on the system. I've tried using the formulas for rotational kinetic energy and factoring in loss by adding a tangential component or a radial component to the right hand side to find out what the lost energy is but I'm stuck.

Am I thinking from the wrong angle? (hehe)

Thanks for any hints in the right direction.

Unless you are given information about the lump of clay falling some distance or with some velocity, you may assume it had no kinetic energy before sticking. Using the angular velocities you can calculate the total kinetic energy before and after the clay sticks to the turntable. If the kinetic energy changes, the difference had to be converted into some other form of energy, and that would be thermal energy in this case. You don't need to know anything about the forces, which is a good thing because you have no way of finding them.

In collisions we often find that some of the initial energy of the objects gets converted into other forms of energy, unless the interaction is completely elastic, which is not the case here. Since the two objects stick together after the collision we classify the collision as completely inelastic. In this case a lot of energy will be converted to heat by the deforming lump of clay.

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Awesome, that points me in the right direction.

esalbred said:
Awesome, that points me in the right direction.

Since you already have the new angular velocity of the turntable+lump system, you can easily calculate its kinetic energy and compare it with the initial energy. :)

The difference between the two is what's been converted to heat.

For an object rotating about its center of mass, the rotational kinetic energy is given by: $$E_k=\tfrac{1}{2}I\omega ^2$$

EDIT: OOF, didn't notice I was necroposting, my apologies.

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What is "Loss of rotational energy to thermal energy"?

Loss of rotational energy to thermal energy refers to the process by which rotational energy, which is the energy associated with an object's rotation, is converted into thermal energy, which is the energy associated with the random motion of particles. This happens when an object experiences friction or resistance as it rotates, causing its rotational energy to be converted into heat.

What causes loss of rotational energy to thermal energy?

The main cause of loss of rotational energy to thermal energy is friction. When an object rotates, it experiences resistance from its surroundings, which causes its rotational energy to be converted into heat. This can also happen due to other factors such as air resistance, drag, and imperfections in the object's surface.

Is loss of rotational energy to thermal energy a reversible process?

No, loss of rotational energy to thermal energy is an irreversible process. This means that once rotational energy is converted into thermal energy, it cannot be converted back into rotational energy. This is due to the second law of thermodynamics, which states that energy cannot be completely converted from one form to another without some loss of usable energy.

What are the consequences of loss of rotational energy to thermal energy?

The consequences of loss of rotational energy to thermal energy depend on the specific situation. In some cases, it can lead to a decrease in the object's rotational speed, which can affect its performance or functionality. In other cases, it can cause the object to heat up, which can lead to issues such as overheating or damage to the object or its surroundings.

How can loss of rotational energy to thermal energy be minimized?

Loss of rotational energy to thermal energy can be minimized by reducing friction or resistance in the object's environment. This can be achieved through lubrication, using smoother surfaces, or reducing the object's speed. Additionally, using materials with higher thermal conductivity can also help dissipate the heat generated from the loss of rotational energy.

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