Dynamics: rogid bodies force and acceleration

  • Thread starter etotheix
  • Start date
  • #1
21
0

Homework Statement



[PLAIN]http://img135.imageshack.us/img135/1063/1763o.jpg [Broken]

Homework Equations



[itex]IG = (1/12)ml^2[/itex]
[itex]\sum Ma=(IG+m(rG)^2)[/itex]

The Attempt at a Solution



I take the moment about A, which gives me the following:
[itex](4kg)(9.81m/s^2)(1m)=((1/12)(4kg)(2m)^2+(4kg)(1m)^2)\alpha[/itex]
[itex]\alpha = 7.3575 rad/s^2[/itex]

But in the solutions they have: [itex]\alpha = 14.7 rad/s^2[/itex], which is 2 times more. They are taking the moment about G, using [itex]Fa = (1/2)(4kg)(9.81m/s^2)[/itex]. Why does it yield a different answer? The way I do it must be wrong, but I don't see why.

Also they have [itex](aG)y = 4.905m/s^2[/itex], but I though that [itex](aG)y = rG*\alpha[/itex], and [itex]rG = 1m[/itex] in this case, so [itex](aG)y[/itex] must be equal to [itex]\alpha[/itex]

What am I doing wrong? Thanks in advance for the help.
 
Last edited by a moderator:

Answers and Replies

  • #2
558
1
Honestly, I don't understand this formula:
[itex]\sum Ma=(IG+m(rG)^2)[/itex]
 
  • #3
tiny-tim
Science Advisor
Homework Helper
25,836
251
hi etotheix! :smile:
I take the moment about A …

no, you can't do that, the Iω formula for https://www.physicsforums.com/library.php?do=view_item&itemid=313" about either the centre of mass or the centre of rotation …

A is neither :redface:

(because A will start accelerating upwards as soon as the string is cut)
Also … I though that [itex](aG)y = rG*\alpha[/itex], and [itex]rG = 1m[/itex] in this case, so [itex](aG)y[/itex] must be equal to [itex]\alpha[/itex]

no, a = rα assumes that r is the distance to the centre of rotation, and (again) that isn't A, so it isn't :wink:

you'll need to use the https://www.physicsforums.com/library.php?do=view_item&itemid=189" force, before and after (just call it F)
Honestly, I don't understand this formula:
[itex]\sum Ma=(IG+m(rG)^2)
[/itex]

it's the parallel axis theorem in disguise :biggrin:
 
Last edited by a moderator:
  • #4
21
0
Thank you very much tiny-tim! It is very clear now.
 

Related Threads on Dynamics: rogid bodies force and acceleration

Replies
7
Views
2K
  • Last Post
Replies
1
Views
2K
Replies
4
Views
798
  • Last Post
Replies
9
Views
9K
  • Last Post
Replies
11
Views
8K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
4
Views
677
  • Last Post
Replies
23
Views
10K
Top