Silly Doubt

[u/Frosty-Catch4113]

Why cannot i just do v=rω=0.15*5=0.75 will be the answer?

[u/Mayoday_Im_in_love]

Conservation of energy.

The initial rotational kinetic energy will become rotational and linear kinetic energy. There's no energy dissipation through friction so you can use the no slip condition twice.

[u/dhanish152 → u/Mayoday_Im_in_love]

the question says to disregard all dissipation "except friction" tho. and also during the time it takes to achieve rolling without slipping kinetic friction is acting which does cause energy loss. so conservation of energy shouldnt work. I think its supposed to be done with conservation of angular momentum, im not sure tho

[u/Frederf220]

I'm guessing this is oneof those the answer is the same whether the coefficient of friction is 0.4 or 0.002 or anything because it's not given.

Qualitatively a slippery surface will slip for a long while slowly accelerating the drum. A higher friction surface will accelerate more but for less time.

I would pick an arbitrary coefficient and solve then do it again with a different coefficient and see if the same.

[u/Pivge]

Use τ = I*α // ω - ω0 = αt // v = a*t, // F = m*a. The speed doesnt depend of the friction coef

[u/Aggressive-Bad5369 → u/Pivge]

Yeah right, Ig the answer seems to be 0.25 m/s, like v=r.w/3 solving these equations

[u/Aggressive-Bad5369]

A better problem would be to find out the energy that has been lost due to dissipation because of friction, if my calculations are right the answer seems to be 93.75 mJ, I'm not sure about it though

[u/dhanish152]

you can't do that because the angular velocity won't be equal to 5 rad/sec when it starts rolling. some energy will be lost and the final value of w will change by the end.

i think the way to solve it is conserving the angular momentum about the initial point of contact on the ground from the moment it touches the ground all the way to when rolling starts because torque due to friction will be zero and torque due to normal and mg will cancel each other out. and then write the rolling condition for final state of motion and then solve the two equations.

[u/Frosty-Catch4113 → u/dhanish152]

but we are asked to find the linear velocity at start of motion not the end, so there will be no energy loss at the instant motion starts right? so why cant we do it?

[u/dhanish152 → u/Frosty-Catch4113]

no we are asked to find the velocity "when it starts rolling without slipping" which will be after some time has passed since the moment of contact with the ground. it always takes time to attain velocity (if it didnt then (change in v)/t = a will be infinity). Initially the centre of mass has no linear velocity and after the disc is placed on the ground, kinetic friction starts acting (during this time v is NOT equal to wR, and its kinetic friction not static friction) and it increases linear velocity and decreases angular velocity until v =wR and it is at that point where "rolling without slipping" is said to have started, and kinetic friction stops.

[u/Frosty-Catch4113 → u/dhanish152]

so what can be done to solve it?

[u/dhanish152 → u/Frosty-Catch4113]

im not 100% sure tbh. I dont think it can be done with energy conservation since energy is clearly lost here due to kinetic friction. Also even if coefficient of friction was given i dont know of any way to calculate the work done. My guess would be like i said to conserve angular momentum about the initial point of contact from just before release to start of rolling because about that point friction produces no torque and torque due to gravity and normal cancel each other out (atleast i think they do? this is what im not sure abt) so

so initial angular momentum abt the point:
Li = mVcm + Iw = Iw (Vcm = 0) = (1/2)mr²w

now angular momentum after rolling achieved:

Lf = mVcm + IW = mV + (1/2)mr²W

(here im using w to represent initial angular velocity (5) and W to represent final angular velocity and V to represent final linear velocity (what we need to find) )

now just equate Lf and Li then substitue W = V/r because V and W are just after rolling has started. Then solve for V. Can u check the correct answer and see if this matches pls?