Question

Finding the angular speed of a cylinder rotating with the force of a string.

Answer 1

Okay.
So w (angular v) = v (linear) / r
w = 1.247 / 0.12 m
w = 10.391 which is incorrect
I feel like I have to do something to account for the force of the string on the cylinder? I suppose I could solve for T somehow as T = 2pi / t but yeah.

Answer 2

"w (angular v) = v (linear) / r "

that relation only works if something is ROLLING without slip..

in general w = v/r where v = the tangential speed of a particle at a distance r from the centre.
the linear speed mentioned here, is the linear speed of the centre of mass.. so you understand why we can't use that here?

Answer 3

force of 35 N for 0.2m...

to clarify.. it is 0.2 meters right not 0.2 minutes .. correct?

Answer 4

think about torques.. and angular acceleration

Answer 5

Yes, 0.2 meters

Answer 6

I also tried calculating the distance the object slips by converting 0.2m into radians..
So, the relationship between torque and alpha is torque = Moment of Inertia * angular acceleration

Answer 7

And given that w or angular speed is the integral of angular acceleration ..
Should I solve for angular acceleration and integrate using that formula?
Or since a force is acting on the object and we know the mass, solve for the acceleration of the body which is tangential acceleration, use that and I to find torque?

Answer 8

From the way the question is written, I think the best way is to use energy to solve this problem. Do you know how to do it?

Answer 9

Well, I know the relationship between total and components of energy. Ie Kinetic and potential energy = Total

Answer 10

Then you're there. Use work-energy theorem, and it's done.

Answer 11

But I guess I could use the equivalents? Like, m = L, v=w, ..

Answer 12

Would my w just be the provided linear velocity, and my alpha F/m?

Answer 13

I'm not sure where I'd use linear velocity in this case.

Answer 14

Change in total KE = work done by F

Answer 15

1/2mvf-1/2mvi = fd?

Answer 16

Where vi = 0, vf = linear, and d=0.2m?

Answer 17

Sorry, could you explain what I need to do further? I'm a bit confused about where to use linear v versus solving for angular v.

Answer 18

1/2mvf²-1/2mvi² = fd
would be for pure translation.

Actually : KEf = 1/2.m.vf² + 1/2.I.wf²

Answer 19

I find w = 20.8 rad/s

Answer 20

I will plug in the variables and see if my answer is similar to the one you calculated. Thank you so much for helping me! I appreciate it. :-)

Answer 21

Oh, I see what you did with KEf, since it has two components. That makes a lot more sense.

Answer 22

I got the same thing. Thanks so much, again. :)

Answer 23

You're welcome :))