Angular acceleration, velocity, momentum of a door?

Click For Summary
SUMMARY

The discussion revolves around the dynamics of a door modeled as a uniform rod, focusing on angular acceleration, velocity, momentum, and rotational kinetic energy when a force is applied. The door, with a width of 1.00 m and mass of 15.0 kg, experiences an angular acceleration of 13.33 rad/s² when a force of 100 N is applied at its midpoint. The resulting angular velocity is calculated to be 2.7 rad/s, with angular momentum at 3.375 kg·m²/s and rotational kinetic energy at 4.56 J. The time taken for the door to close after being pushed is approximately 0.323 seconds, and various calculations are provided for different points of force application.

PREREQUISITES
  • Understanding of rotational dynamics, specifically torque and angular acceleration.
  • Familiarity with the moment of inertia for uniform rods.
  • Knowledge of kinematic equations for rotational motion.
  • Ability to apply Newton's laws in rotational contexts.
NEXT STEPS
  • Study the concept of torque in rotational dynamics using "Torque and Angular Momentum" resources.
  • Learn about the moment of inertia for various shapes, focusing on "Moment of Inertia for Composite Bodies".
  • Explore kinematic equations for rotational motion, particularly "Rotational Kinematics and Dynamics".
  • Investigate the effects of varying force application points on angular motion, using "Angular Motion with Variable Forces".
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding the principles of rotational dynamics and their applications in real-world scenarios, particularly in mechanical systems involving hinges and levers.

  • #61
Haveagoodday said:
you have to use this equation t= θf-θi/wf-wi
you
haruspex said:
wf-wi? Did you mean that?
yes
 
Physics news on Phys.org
  • #62
haruspex said:
What is the are you putting for alpha here? What units do you have for omega?
That one was closest to theta. 90 degrees.
That is the formula for rotational motion...if alpha is a constant
 
  • #63
Haveagoodday said:
you

yes
I've never seen that equation, and if you were to apply it you would get infinity. w does not change after the force on the door ceases.
 
  • #64
coffeemanja said:
That one was closest to theta. 90 degrees.
That is the formula for rotational motion...if alpha is a constant
You did not answer either question. What number are you plugging in for alpha, and what units is your number for omega expressed in?
 
  • #65
haruspex said:
You did not answer either question. What number are you plugging in for alpha, and what units is your number for omega expressed in?
Alpha is 10 rad/s...agh...I see now! Let me redo here...
 
  • #66
haruspex said:
I've never seen that equation, and if you were to apply it you would get infinity. w does not change after the force on the door ceases.
but i
coffeemanja said:
That one was closest to theta. 90 degrees.
That is the formula for rotational motion...if alpha is a constant
dont forget that you have to use radians instead of degrees. But still it is apparently wrong to use that equation.
 
  • #67
Haveagoodday said:
but i
Yes?
 
  • #68
haruspex said:
I've never seen that equation, and if you were to apply it you would get infinity. w does not change after the force on the door ceases.
well it is kind of like this equation v= dx/dt, and if you rearrange it you get t=dx/dv, and same goes for rotational motion equation w=dθ/dt, at least i think so.
 
  • #69
I got 0.795 s
 
  • #70
Haveagoodday said:
well it is kind of like this equation v= dx/dt, and if you rearrange it you get t=dx/dv.
No, you get dt=dx/v. It is certainly not the case that t=dx/dv.
 
  • #71
coffeemanja said:
I got 0.795 s
Good, if a little inaccurate. (But why does everyone insist on decimals? What's wrong with ##\pi/4##?
 
  • Like
Likes   Reactions: SammyS
  • #72
haruspex said:
Good, if a little inaccurate. (But why does everyone insist on decimals? What's wrong with ##\pi/4##?
Wait... It's pi/2. I do not know, may be because we are used to use SI units..
 
  • #73
coffeemanja said:
Wait... It's pi/2. I do not know, may be because we are used to use SI units..
did you use this equation Θf=Θi+ωi*t+0.5αt^2 ?
 
  • #74
Haveagoodday said:
did you use this equation Θf=Θi+ωi*t+0.5αt^2 ?
Yes!
 
  • #75
coffeemanja said:
Yes!
what are the values you put in?
 
  • #76
Have somebody come to a solution for e)?
 
  • #77
Haveagoodday said:
Have somebody come to a solution for e)?
I assume you are just looking for a yes/no answer. There's a risk your question might be interpreted as a request for a solution to be posted.
 
  • #78
Haveagoodday said:
Have somebody come to a solution for e)?
I think somebody posted an answer for part (e).

I don't know if that counts as a solution.
 
  • #79
Haveagoodday said:
Have somebody come to a solution for e)?
Here's a starting point:

F- Fh = M* a ("h" being in a subscript of F, and "a" being "a" of centre of mass)

I could post whole my work, but I believe It's better for you that you figure it out yourself. But this starting point should be more than enough.
Let me know the result you get in e) and thereby f)
 
  • #80
e) Fh=F(1-3d/(2L))
f) 2L/3
 
  • #81
How did you get C) 0.795 s or pi/4
 
  • #82
  • Like
Likes   Reactions: jimjames
  • #83
jimjames said:
How did you get C) 0.795 s or pi/4
As I said, 0.795 is rather inaccurate.
 
  • #84
haruspex said:
As I said, 0.795 is rather inaccurate.
It is, but where we study they insist on decimal numbers. It is inaccurate, but the main reason why they do it is so we can use our knowledge about significant digits. You'd be surprised over how many people make silly mistakes on significant digits.
 
  • #85
StavangerFinest said:
It is, but where we study they insist on decimal numbers. It is inaccurate, but the main reason why they do it is so we can use our knowledge about significant digits. You'd be surprised over how many people make silly mistakes on significant digits.
No, it's more inaccurate than it should be for a three digit decimal. Calculate pi/4.
 
  • #86
haruspex said:
No, it's more inaccurate than it should be for a three digit decimal. Calculate pi/4.
Oh yeah... 0,785s...Didn't notice that they had nine instead...Sorry, my bad
 
  • #87
Read the book from page 308 to 314, you will understand the physics not just for one question but for all related questions.
 
  • #88
Bambisu said:
Read the book from page 308 to 314, you will understand the physics not just for one question but for all related questions.
The thread is two years old. I doubt StavangerFinest is still interested.
 
  • #89
Heia Anders
 

Similar threads

  • · Replies 17 ·
Replies
17
Views
992
  • · Replies 6 ·
Replies
6
Views
2K
Replies
3
Views
3K
  • · Replies 1 ·
Replies
1
Views
3K
Replies
335
Views
16K
Replies
3
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
8
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
Replies
10
Views
2K