Explanation of an angular momentum term

AI Thread Summary
The discussion centers on understanding the angular momentum term mVfR + Icmω in the context of a solid ball transitioning from sliding to rolling without slipping. The user is confused about how this term is derived and its significance in the problem involving a ball sliding on a surface with friction. They acknowledge the conservation of angular momentum but seek clarity on the specific components of the final term. The problem involves calculating the ball's speed when it starts rolling and the energy lost due to friction. Overall, the user expresses a strong need for help in grasping this concept.
Levi Tate
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Hello, could somebody please explain to me why in 4 of these solutions, the angular momentum final term about point p is mVfR + Icmω ? It is in huge attached solutions my teacher posted.

Thank you very much in advance

Here is the problem in case you are interested of Horne context.

4. A solid ball of radius are initially slides without rotating on a horizontal surface with a variable coefficient of friction. If the initial speed is Vo, find the speed when the ball begins to roll without slipping. Also find the energy lost due to friction
 

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Upright, sorry about this, it looks upright when I upload it..
 

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Come on.. I know you smart cats know what this angular momentum term is all about. PLEASE I AM DESPERATE.
 
Sorry my iPad edited this very poorly...4. A solid ball of radius R initially slides without rotating on a horizontal surface with a variable coefficient of friction. If the initial speed is Vo, find the speed when the ball begins to roll without slipping. Also find the energy lost due to friction
 
I understand the angular momentum is conserved but I don't understand the final term in the angular momentum. I can't find out anything, it's bewildering me.
 

Thread 'Rolling without slipping on a curved surface'

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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Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
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