/sci/ - Science & Math » Thread #14321788

10KiB, 1152x648, rolling ball.png

View Same Google iqdb SauceNAO

Anonymous Mon 21 Mar 04:40:33 2022 No.14321788 View Reply Original Report

Quoted By: >>14321794 >>14322589 >>14323699

How are the mass of the rolling ball, the angle of the surface and the acceleration of the ball through space related to each other? Is there an equation for this?

Assume the ball is made of uniform solid material.

Anonymous

Anonymous Mon 21 Mar 2022 04:47:03 No.14321794 Report

Quoted By:

>>14321788
F=ma same as mg=ma

Anonymous

View Same Google iqdb SauceNAO 1646717449246.webm, 2MiB, 222x400

Anonymous Mon 21 Mar 2022 05:19:56 No.14321838 Report

Quoted By:

>Is there an equation for this?
why wouldnt there be? it isn't too hard to find. I just re-computed it on the back of a paycheck envelope to remind myself i still remember physics 1.
is this a homework thread?

Anonymous

Anonymous Mon 21 Mar 2022 05:21:36 No.14321839 Report

Quoted By:

Su=gma

Anonymous

View Same Google iqdb SauceNAO 1647739616851.png, 2MiB, 1086x1022

Anonymous Mon 21 Mar 2022 05:53:47 No.14321873 Report

Quoted By: >>14322508 >>14323774

$a=\frac{g\sin\alpha}{1+I/mR^2}$
If the ball is a solid sphere, $I/mR^2=2/5$ and $a=\frac{5}{7}g\sin\alpha$

If you cannot derive the above result in less than 3 minutes without googling you are a brainlet

Anonymous

Anonymous Mon 21 Mar 2022 14:18:25 No.14322508 Report

Quoted By:

>>14321873
Yeah it's easy to derive it with all the background knowledge of physics

Anonymous

Anonymous Mon 21 Mar 2022 14:36:03 No.14322542 Report

Quoted By: >>14322547 >>14323699

does it matter whether or not it slips?
my instincts tell me it shouldn't but i don't know how the numbers add up

Anonymous

Anonymous Mon 21 Mar 2022 14:37:20 No.14322547 Report

Quoted By: >>14322561

>>14322542
If it doesn't slip, some of the gravitational potential energy converts to rotational energy. Otherwise it all goes to linear kinetic energy.

Anonymous

Anonymous Mon 21 Mar 2022 14:41:36 No.14322561 Report

Quoted By:

>>14322547
yeah, so i guess the linear acceleration would be greater with slip, since less energy is converted to rotational

Anonymous

Anonymous Mon 21 Mar 2022 14:51:31 No.14322589 Report

Quoted By: >>14322637 >>14323223

>>14321788
All you need is conversation of energy.
$m g y = \frac{m}{2} v^2 + \frac{I}{2} \omega ^2$
For the moment of innertia you have to calculate a triple integral but you can just look up the answer as the formula is common knowlodge.
$I = \frac{2}{5} m R^2$
So
$m g y = \frac{m}{2} v^2 + \frac{m}{5} R^2 \frac{v^2}{R^2} = \frac{7m}{10} v^2$
Now differentiate after the time with the chain rule.
$m g \dot y = \frac{7m}{5} v a$
Note that $\dot y = \sin(\alpha) v$ so
$a = \frac{5}{7} \sin(\alpha) g$

Anonymous

Anonymous Mon 21 Mar 2022 15:08:43 No.14322637 Report

Quoted By:

>>14322589
so happy to wake up and see I forced someone else to work through this boring problem

Anonymous

Anonymous Mon 21 Mar 2022 15:43:53 No.14322741 Report

Quoted By: >>14322927 >>14323856

Why do you beta cucks keep helping these retards with their homework? You think theyre going to pat you on the back?

Anonymous

Anonymous Mon 21 Mar 2022 17:02:52 No.14322927 Report

Quoted By:

>>14322741
solving, banging out physics 1000 level problems gives me a fucking rush thats why

Anonymous

Anonymous Mon 21 Mar 2022 18:31:12 No.14323223 Report

Quoted By: >>14323252 >>14323647

>>14322589
Are you saying that the mass doesn't matter?

Anonymous

Anonymous Mon 21 Mar 2022 18:40:53 No.14323252 Report

Quoted By: >>14324469

>>14323223
Mass doesn't matter, moment of inertia does.

Anonymous

Anonymous Mon 21 Mar 2022 21:00:49 No.14323647 Report

Quoted By: >>14323810

>>14323223
Not as long there is no friction.

Anonymous

Anonymous Mon 21 Mar 2022 21:17:50 No.14323699 Report

Quoted By:

>>14321788
>>14322542
>>14322542
It matters whether it rolls or not and whether it slips or not and how much.

No Roll $(\omega = 0)$
$K_R / K_T = 0$
$a = g\sin{\phi}$

Sliding Roll $(0 \lt \omega \lt v R)$
$0 \lt K_R / K_T \lt I / m R^2$
$g \frac{\sin{\phi}}{1+I / m R^2} \lt a \lt g\sin{\phi}$

No-Slip Roll $(\omega = v R)$
$K_R / K_T = I / m R^2$
$a = g \frac{\sin{\phi}}{1+I / m R^2}$

Slipping Roll $(v R \lt \omega)$
$I / m R^2 \lt K_R / K_T$
$a \lt g \frac{\sin{\phi}}{1+I / m R^2}$

Anonymous

Anonymous Mon 21 Mar 2022 21:45:07 No.14323774 Report

Quoted By: >>14323794

>>14321873
>If you cannot derive the above result in less than 3 minutes without googling you are a brainlet
Brainlet here. Please show me wind resistance and the increased friction due to turbulence as a function of the accelerated cylinder rotation.

Anonymous

Anonymous Mon 21 Mar 2022 21:50:32 No.14323785 Report

Quoted By: >>14323799

It is the density of the ball that determines how fast it will roll down the slope, not "gravity".
On a steep slope the density of a ball is larger than on a gentle slope.

Anonymous

Anonymous Mon 21 Mar 2022 21:53:24 No.14323794 Report

Quoted By:

>>14323774
>Brainlet here. Please show me wind resistance and the increased friction due to turbulence as a function of the accelerated cylinder rotation
The above result neglects all effects of air, brainlet

Anonymous

Anonymous Mon 21 Mar 2022 21:54:25 No.14323799 Report

Quoted By:

>>14323785
LMAO

Anonymous

Anonymous Mon 21 Mar 2022 21:57:54 No.14323810 Report

Quoted By:

>>14323647
rolling without slipping implies friction, brainlet

Anonymous

Anonymous Mon 21 Mar 2022 22:21:31 No.14323856 Report

Quoted By:

>>14322741
>Be me
>Help retards on /sci/
>I brush off the rust of basic physics
>I actively harm the retards by giving them answers which I know they won't rederive themselves
What's the problem? I'm helping myself and hurting them.

Anonymous

Anonymous Tue 22 Mar 2022 03:03:13 No.14324469 Report

Quoted By:

>>14323252
Oh yeah, I can kind of see why. You would think intuitively that a greater mass would accelerate slower. But at the same time it also has greater potential energy so it makes sense.

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches