Putting rotating cylinder on the ground

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A cylinder with a radius of 0.1m and an initial angular velocity of 10 revolutions per second is placed on horizontal ground, and the goal is to determine the time it takes to roll without slipping, given a coefficient of friction of 0.1. The moment of inertia and the relationship between linear and angular acceleration are key to solving the problem. The correct time calculated for the cylinder to roll without slipping is 2.09 seconds. Clarification was made regarding the angular frequency, as the initial value provided was actually the usual frequency in revolutions per second. The discussion confirms the accuracy of the solution with the adjusted understanding of frequency.
srecko97
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Homework Statement


We put a cyllinder with unknown mass and radius 0.1m which rotates with angular velocity 10 /s around its geometric axis on the horizontal ground. After what time does the cyllinder roll without slipping? Coefficient of friction is 0.1.

Homework Equations


F=ma
M=J ⋅ ∝

The Attempt at a Solution


J- moment of inertia, k-coefficient of friction ... a* - acceleration of center of mass[/B]
image.jpg


image.jpg

The result should be 2.09 s. Please correct me!
 
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Are you sure you've stated the problem correctly? Your answer looks right to me.
 
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I have just realized that everything is OK except the value for angular frequency. The given frequency is not the angular (which I thought) but the usual frequency (number of turns per second)
 
srecko97 said:
I have just realized that everything is OK except the value for angular frequency. The given frequency is not the angular (which I thought) but the usual frequency (number of turns per second)

Of course!
 
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Thread 'Correct statement about size of wire to produce larger extension'

Thread 'Correct statement about size of wire to produce larger extension'

The answer is (B) but I don't really understand why. Based on formula of Young Modulus: $$x=\frac{FL}{AE}$$ The second wire made of the same material so it means they have same Young Modulus. Larger extension means larger value of ##x## so to get larger value of ##x## we can increase ##F## and ##L## and decrease ##A## I am not sure whether there is change in ##F## for first and second wire so I will just assume ##F## does not change. It leaves (B) and (C) as possible options so why is (C)...
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