Drums rolling downhill scenario

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In summary, the drum with its mass at the center will reach the ground first due to its lower angular inertia compared to the other drums. This principle is related to the concept of inertia and how it affects the movement of objects. The drum with the larger surface area may face more friction, but its lower angular inertia allows it to reach the ground faster. This can also be seen in the example of the pizza drum, where the drum with its mass at the center will reach the ground first due to its lower angular inertia compared to the other drum with missing slices.
  • #1
Skhandelwal
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All the drums weigh the same...one has greater surface area , one has center of mass in the middle...and one has center of mass at an end.

Which will get to the ground first?

When I think I am starting to understanding mechanics, I spot questions like these... If I am having problem w/ this...what principle am I weak on?
 
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  • #2
The force is the component of gravity that is parallel to the angle of the inclined plane (cos(angle)). The resistance to this force is the inertia of the drums, which is a combination of the linear and angular inertias. Since the drums have the same mass, the linear inertia is the same for the drums, so the only difference is the angular inertia. See if you can figure it out from here.
 
  • #3
The one w/ the bigger area will get at the bottom first...even though, it has to face more friction...the surface area makes up for it. Btw, is the center of mass faster or the one which has the mass at a corner?

Also, another similar question, if there is a drum, and then there is another drum but there is one difference. Assume the drum is a pizza made up of 16 slices. Well, every alternative slice has been taken out. Which one will get to the ground first?
 
  • #4
The fastest drum is the one with it's mass at it's center. The surface area doesn't mattter unless you're including friction from the air. If the mass is at the center, then there's virtually no angular inertia.
 

1. What is the "drums rolling downhill scenario"?

The "drums rolling downhill scenario" is a thought experiment that explores the concepts of energy transformation and conservation. In this scenario, a series of drums are placed on a hill and allowed to roll down. As they roll, their potential energy (due to their height on the hill) is converted into kinetic energy (due to their motion). The question is, what happens to all of that energy once the drums reach the bottom of the hill?

2. How does this scenario relate to real-world physics?

The "drums rolling downhill scenario" is a simplified version of many real-world situations that involve energy transformation and conservation. For example, when a car drives down a hill, its potential energy is converted into kinetic energy. Similarly, when a ball is thrown into the air, its kinetic energy is gradually converted back into potential energy as it reaches its maximum height.

3. What are the key concepts being explored in this scenario?

The main concepts being explored in this scenario are potential energy, kinetic energy, and energy conservation. Potential energy is the energy that an object possesses due to its position or state, while kinetic energy is the energy of motion. The scenario also highlights the principle of energy conservation, which states that energy cannot be created or destroyed but can only be transformed from one form to another.

4. What are some real-world applications of these concepts?

The concepts of potential energy, kinetic energy, and energy conservation have numerous applications in everyday life. For example, understanding these concepts is crucial for engineers when designing roller coasters or other amusement park rides. These concepts are also important in the field of renewable energy, where energy transformation and conservation are essential for harnessing and utilizing various sources of energy.

5. How does this scenario relate to the laws of thermodynamics?

The "drums rolling downhill scenario" is directly related to the first and second laws of thermodynamics. The first law, also known as the law of conservation of energy, states that energy cannot be created or destroyed. This law is evident in the scenario as the total amount of energy (potential + kinetic) remains constant throughout the drums' descent. The second law of thermodynamics, on the other hand, states that in any energy transformation, some energy will always be lost in the form of heat. This can be observed in the scenario as some of the drums' energy is lost due to friction and air resistance as they roll down the hill.

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