How Does a Time-Varying Force Affect Angular Momentum in a Dual-Radius Spool?

[Yash123]

Homework Statement

a spool of radius R1 and R2 (R2>R1) is kept on hortizontal surface. A force f= 2t N (where t is time ) acts on the inner radius tagentially find the angular momentum of the system about the bottomost point of the spool.

Homework Equations

v=u+at
W=Wi+alpha(t)
L=IW+mvr

The Attempt at a Solution

but the answer is t^2(R1+R2)

 

[Let'sthink]

Where is the pool fixed at the center or at the indicated point?

 

[Yash123]

Where is the pool fixed at the center or at the indicated point?

It's not fixed ...it's on the floor free to rotate and translate

 

[LemmeThink]

Frankly, your work is illegible.

Nonetheless, could you give me the relation between ## \vec v## and ##\vec a##, and that between ##\vec α## and ##\vec ω##?

 

[Yash123]

Frankly, your work is illegible.

Nonetheless, could you give me the relation between ## \vec v## and ##\vec a##, and that between ##\vec α## and ##\vec ω##?

Frankly, your work is illegible.

Nonetheless, could you give me the relation between ## \vec v## and ##\vec a##, and that between ##\vec α## and ##\vec ω##?

I solved it just used the wrong equations ...!

 

[Yash123]

It's not fixed ...it's on the floor free to rotate and translate

but can you please solve iit jee paper 2 2016 rbd question

 

[haruspex]

Homework Statement

View attachment 107579
a spool of radius R1 and R2 (R2>R1) is kept on hortizontal surface. A force f= 2t N (where t is time ) acts on the inner radius tagentially find the angular momentum of the system about the bottomost point of the spool.

Homework Equations

v=u+at
W=Wi+alpha(t)
L=IW+mvr

The Attempt at a Solution

View attachment 107580
but the answer is t^2(R1+R2)

In your calculation of the linear acceleration you have ignored friction at the ground. Not sure if you did the same with the moments.
Please do not post working as images. Use images for diagrams and textbook extracts. Take the trouble to type in your algebra.

 

[Yash123]

In your calculation of the linear acceleration you have ignored friction at the ground. Not sure if you did the same with the moments.
Please do not post working as images. Use images for diagrams and textbook extracts. Take the trouble to type in your algebra.

I solved it

 

[Let'sthink]

You say F = 2t what about direction? Then you want angular momentum at what time. If time varying force is acting neither the momentum nor angular momentum will be constant.

 

[Yash123]

You say F = 2t what about direction? Then you want angular momentum at what time. If time varying force is acting neither the momentum nor angular momentum will be constant.

Thanks for the reply but I solved it