You yank on the end of the toilet paper roll fast enough to tear off a small length. Roll A has more paper on it than Roll B.
In which case is it easier to do this?
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An object with a greater mass does not necessarily have a greater rotational inertia. Also, you have not considered the difference in torque.
how about torque
The roll, when fuller, has more mass and more diameter, so its moment of inertia is greater. So it will not try to rotate easily which helps to tear off the roll. When lighter and smaller in diameter hat is with less moment of inertia the roll rotate readily without offering much resistance to the yank force.
in which sense it's easier? Using less force or more force. I need a free body diagram and ;let's suppose a paper weighs nothing and we use F force so F=Tension (T) Also tension creates rotional motion T=Iw and do your job it's option B
In my opinion, the question is poorly worded. When I started with this question, I tried to read the explaination carefully to gauge exactly what it wanted. And it clearly seems to be asking in which situation it possible to yank fastest - "you yank the toilet paper roll fast enough... in which case is it easier to do this". It strikes me that in a situation with less resistance, it would be easier to yank faster!
Anyway, I went with my instincts and selected A, which was correct, so I'm not complaining... but, well, I guess I'm still a little miffed at how much time I wasted on it!
The torque exerted on roll A is greater which would cause the roll to angularly accelerate rather than allow for paper to be torn off. The rotational inertia of roll A is also greater, which would tend to keep the roll from angularly accelerating. However, torque is proportional to radius and rotational inertia is proportional to the square of the radius. So the increase in rotational inertia is the more significant effect, making it easier to rip paper from roll A. This is easy to demonstrate with actual rolls of toilet paper. (Roll A also has a higher mass which increases it's rotational inertia even more.)
why is torque on roll A greater?
Well, its about inertia, as its more when the roll is full
Then it would be difficult right.the question is about easier one.
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No, less difficult because it will not spin as easily and tear more easily instead.
The greater mass will also create more friction of between the T.P. core and the metal holder which further validates A as the correct answer.
Just took a poo so many times this week that this was easy to remember
It has to do with torque, but common sense says the heavier one requires less force to create a turning effect since it's own weight has generated most.
I feel the same intuitively
It's own weight on the side away from you will be working against you.
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Exactly, but since it has a greater moment of inertia, it will tend to keep its form, shape and position thus, the effort you make will cause it to spin easily, however for a lighter one, you have to add more effort to ensure it doesn't fall(change position) and form. in order to ensure these properties are favourable i feel it demands alot from you than the heavier one will.
Points for A (in basic terms)
More Mass more inertia +1 )( Greater radius greater torque -1 )(Kevin disclaimed the torque though so +1
I would add that friction in a real situation could also be a big factor but again this would support the heavier roll +1 Points for A=2
Finally, my habbit's being useful. I gone through a lot of toilet paper rolls and I did that all the time, according to my observation, bigger roll is heavier so it takes more force to get it rolling, so it has more resistance.
A. Here is why: If an item has a larger mass, then it's rotational inertia will be larger. Hence, it will be harder to make a full(heavier) roll to spin by pulling it, so it will be easier to tear the piece of paper off.
Should include a choice for no difference for completeness. It is Roll A because it has more rotational inertia both from being more massive and having a greater radius.
The larger roll has more mass and will offer more resistance to movement for 2 reasons. Inertia and friction against the wall. The resistance to movement makes it more likely to tear than just unroll.
But why can’t you use two hands? But if this person had whatever case to use one hand answer ,A’ would’ve been better because if the roll is bigger the smallness of a piece is bigger than by a small roll, so for example if you take the same length of toilet paper it will seem bigger in the larger roll, and smaller in the smaller roll.
This is not a solution; this sounds more like a report.
My answer was Incorrect. My understanding was the torque required in B is less compared to A due to smaller radius. Why not right?
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It has more to do with inertia than torque. See X's solution (the most upvoted one).
I just thought about a moment (force times a distance) and imagined a free body diagram. The larger roll had a longer distance from the tube, so it required less (downward) force compared to the smaller roll when trying to accomplish the same result.
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If an item has a larger mass, then it's rotational inertia will be larger. Hence, it will be harder to make a full(heavier) roll to spin by pulling it, so it will be easier to tear the piece of paper off.