Effect of moment of inertia on rolling distance

In summary: A disk will experience more drag because it has more surface area, while a hoop will experience less drag because it has a smaller surface area. This difference in drag may cause the disk to roll further than the hoop.
  • #1
Poligon
23
0
Hi everyone, good day. this might be a simple question, but I need someone to check my answer.
A disk and a hoop, of same mass and same diameter, is first giving a torque (same amount of torque for both) then the torque is removed (the torque is acting on them for the exact same period of time), causing them to roll freely without slip. The question is, which one will roll further?
My answer to the question will be, both will roll the same distance. However, the disk will arrive at the end point first while the hoop will arrive at the end point later. Other than that, the disk will achieve higher maximum linear velocity in the process.
Is my answer correct? This is because they are being given same amount of energy. thus the distance they can roll should be the same.
Other than that, due to the different in mass moment of inertia, the rotational kinetic energy to translational kinetic energy ratio for disk and hoop is different. I am actually curious on what does this ratio implies? Higher ratio means more energy given is being converted to rotational KE, so? what does higher rotational KE implies? It got to be have effect on something, like the traveling time, the distance traveled, something like that. Can anyone relates these to me? Thank you very much for your time!
 
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  • #2
Hi everyone, First of all, I am very sorry that I misplaced the post.
Next, I noticed that the question is viewed by 135 people, but no replies. Am I not putting enough effort in solving my question? But i think i have first answered my question right?
I am new here, so please tell me if i overlooked any rules.
I really wish to know the answer to the questions.
Thank you!
 
  • #3
If the only force acting on the rolling objects is friction with the surface they roll upon, then I think your answer is correct. However, if you take drag into consideration, things may be different.
 

Related to Effect of moment of inertia on rolling distance

1. How does the moment of inertia affect the rolling distance of an object?

The moment of inertia is a measure of an object's resistance to changes in its rotational motion. In terms of rolling distance, a higher moment of inertia means that the object will require more torque or force to start rolling, resulting in a shorter rolling distance. On the other hand, a lower moment of inertia means that the object can start rolling with less torque or force, resulting in a longer rolling distance.

2. What factors determine the moment of inertia of an object?

The moment of inertia of an object depends on its mass and its distribution of mass relative to its axis of rotation. The farther the mass is from the axis of rotation, the higher the moment of inertia will be. Additionally, the shape of the object also plays a role in determining its moment of inertia. Objects with a larger radius or a more spread out mass distribution will have a higher moment of inertia.

3. How does the shape of an object affect its moment of inertia?

The shape of an object has a significant impact on its moment of inertia. Objects with a larger radius or a more spread out mass distribution will have a higher moment of inertia. This is because the mass is farther from the axis of rotation, resulting in a greater resistance to changes in rotational motion. On the other hand, objects with a smaller radius or a more compact mass distribution will have a lower moment of inertia.

4. Can the moment of inertia be changed?

Yes, the moment of inertia can be changed by altering the mass or mass distribution of an object. For example, adding weight to the outer edge of a rotating object will increase its moment of inertia, while removing weight from the outer edge will decrease its moment of inertia. Additionally, changing the shape of an object can also impact its moment of inertia.

5. How does the moment of inertia affect the rolling distance of different objects?

The moment of inertia affects the rolling distance of different objects in different ways. Objects with a higher moment of inertia will have a shorter rolling distance, while objects with a lower moment of inertia will have a longer rolling distance. This can be observed in objects of the same mass and shape, but with different mass distributions. For example, a solid sphere will have a higher moment of inertia and a shorter rolling distance compared to a hollow sphere with the same mass, but a lower moment of inertia.

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