Velocity of centre of mass (rolling w/o slipping)

AI Thread Summary
To find the velocity of the center of mass of a glass marble rolling down a 10-degree ramp without slipping, one must consider the conversion of potential energy to kinetic energy. The moment of inertia for a sphere is given as 2/5MR^2, which is essential for calculating rotational motion. The discussion emphasizes the relationship between linear velocity and rotational motion, suggesting that potential energy can be transformed into both translational and rotational kinetic energy. Participants encourage using the problem template for clarity and suggest connecting concepts of energy and motion for a comprehensive understanding. A clear approach to solving the problem involves applying energy conservation principles.
redtrebor
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Find the velocity of the centre of mass of a glass marble which rolls from rest down a
gentle ramp inclined at an angle of 10o
to the horizontal, without slipping, after it has
travelled for a distance of 2.3 m.



Moment of inertia of sphere: 2/5MR^2



Past paper question that I'm really struggling with.
 
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Hi treb, and welcome to PF.
How did you bypass the template ? Folks at PF don't enforce it strictly to pester you! Use it and you'll get answers.
 
Hi, that was as close to the template as i could manage I'm afraid. I really don't know where to start with this question
 
I need a bit more to help you adequately. Ever heard of potential energy ? Can you connect rotation and velocity of center of mass with each other ?
 

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Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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