(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A coin stands vertically on a table. It is projected forward (in the plane of itself) with speed v and angular speed w. The coefficient of kinetic friction between the coin and the table is u. What should v and w be so that the coin comes to rest (both translationally and rotationally) a distance d from where it started.

2. Relevant equations

I = 1/2mr^2

T = r x f

Ff = uFn

F = ma

T = Iw’

3. The attempt at a solution

For v:

Ff = uFn

Ff = umg

Fnet = umg

ma = umg

a = ug

v - ug(t) = 0

v - ug(d/v) = 0

v = (ugd)/v

v^2 = ugd

v = sqrt(ugd)

For w:

T = r x f

T = umgr

T = Iw’

umgr = 1/2mr^2w’

w’ = 2ug/r

w - (2ug/r)(t) = 0

w = (2ug/r)(d/v)

w = (2ug/r)(d/(sqrt(ugd)))

w = 2sqrt(ugd)/r

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# Homework Help: Angular velocity and friction

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