A uniform disc of radius R is placed on a rough horizontal surface and given a linear horizontal velocity v₀ and angular velocity ₀ as shown.The disc comes to rest after moving through some distance to right,it follows that:

a) v₀=w₀R

b)2v₀=w₀R

c)2v₀=3w₀R

d)3v₀=2w₀R

looking for both the answer as well as the method...

even i have this doubt.How do you do this? some one please reply!

I think the ans is (b)2v₀=w₀R.Let us denote angular acc. by k and coeff. of friction by p.

Let it come to rest after time t,then w₀=kt and v₀=pgt.

Using torque eqn.,f.R=I.k=(1/2)mR²kpmg=mRk/2k=2pg/R.

Substituting this,Rw₀=2pgt=2v₀.

ok thanks...

but how would you solve this sum using energy conservation?

srry But I dont agree with u frnd-"Energy conservation is not applicable in presence of dissipiative forces-here its friction"

bt Angular momentum abt the bottomost pt is conserved:bcoz torque of mg,N,frictn is zero(they all pass thr the contact pt)

Initial angular momentum=Iw-mv_oR=3/2mR²w_o-mv_oR

Final angular momentum=0(as the disc stops)

equating the two  we get

2v₀=3w₀R  (c) Ans

ok but i had asked this ques to my sir and he told me to use energy conservation even i had thouught that because friction is acting energy wont be conserved but im very confused.

yes the energy can be conserved as in pure rolling the wok done by friction is zero provide it should perform pure rolling and as the surface is rough i think it would do pure rolling and so the ans can be found by energy conservation.

correct me if i m wrong.

yeah but over here the body is not pure rolling..

how can u tell that it is not purely rolling

plz explain`

@animal

its no where given that frictn is sufficient to prevent slipping //the disc is performing pure rolling

yes @akku i got it now it can be solved by ang momentum conservation abt the lowest pt as u havehave done

thanx.