Question on Rotational Dynamics

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A uniform disc with radius R rotating at angular velocity w will come to rest on a rough table in a time given by the formula (3RW)/(4ug), where u is the coefficient of sliding friction and g is the acceleration due to gravity. The discussion emphasizes the relationship between changes in kinetic energy (K), potential energy (U), and work done by friction (W), expressed as ΔK + ΔU = W_friction. Participants clarify that work done by friction can be calculated using the formula Fd cos(angle), with considerations for angular displacement. There is a reminder that complete solutions to homework questions should not be provided without the questioner showing prior effort. The conversation highlights the importance of understanding the principles of rotational dynamics and the role of friction in motion.
alamin
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1.A uniform Disc of Radius R is rotating in its own plane with angular velocity w when it is placed flat on a rough table. If u the coefficient of sliding friction is independent of velocity show that the time taken for the disc to come to rest is
(3RW)/(4ug). How does the kinetic energy of rotation of the disc vary with time?
 
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ok please show us what work you have done. we arent going to solve (although we can) your problems for you
also for your problems remember that
\Delta K + \Delta U = W_{friction}
where K represnets kinetic energy
U represnts potential energy
and W represents work
and delta is the change
 
May I know what is the formula to calculate work done by frcition? Displacement is given in the case, but the friction force is not.
 
work done is F d cos(angle)
if angular then d = (angular displacement)
 
stunner5000pt said:
work done is F d cos(angle)
if angular then d = (angular displacement)
I thought the work done by the friction force is \int \vec{\tau} \cdot d\vec{\theta}?
 
Last edited:
Psi-String,

We appreciate that you are willing to assist, but please do not offer complete solutions to homework questions.

Just to remind everyone, the Homework Help section of the PF Global Guidelines says the following:

On helping with questions: Any and all assistance given to homework assignments or textbook style exercises should be given only after the questioner has shown some effort in solving the problem. If no attempt is made then the questioner should be asked to provide one before any assistance is given. Under no circumstances should complete solutions be provided to a questioner, whether or not an attempt has been made.[/color]
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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