Moment of inertia for a door help

AI Thread Summary
To determine the moment of inertia for a 19kg door hinged along its long side, the approach involves treating the door as a series of thin vertical slices. Each slice's mass can be calculated based on its width and height, with the distance from the hinge being a critical factor in the calculation. The integral I = ∫(R^2 dm) is used to sum the contributions of each slice, where R is the distance from the hinge. The discussion highlights the challenge of applying calculus to this 2D object, particularly in deriving the mass element dm. Seeking examples or guidance on similar problems can aid in understanding the process.
ahello888a
Messages
23
Reaction score
0

Homework Statement


Determine the moment of inertia of a 19kg door that is 2.5m high and 1.1m wide and is hinged along long side. Ignore the thickness of the door


Homework Equations



I=\int (R^2 dm)

The Attempt at a Solution


I really don't know where to start with this problem. My book only shows me how to do moments for cylindrically shaped objects and rods, so i don't know how to deal with 2d objects. I'm having particular trouble with coming up with a dm that is reliant on R.
 
Physics news on Phys.org
The general definition of moment of intertia is to consider a small part of the object with mass dm at a distance r and sum the product of r*r dm.
So for the door, imagine splitting the door into thin vertical slices, then calculate the mass of the slice and the square of the distance from the hinge.
If you know calculus you can do this analytically and come up with an equation - that's what the integral you have given calculates
 
i still have absolutely no clue how to do this. can you point to an example or something?
 
never mind...
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Rotational inertia of square about axis perpendicular to its plane
2
Replies
52
Views
4K
Moment of inertia of a disc using rods as differential elements
Replies
8
Views
2K
Moment of inertia of a cuboid parallel to one of its faces (repost with diagram)
Replies
25
Views
2K
Moment of inertia of door rotation
Replies
1
Views
3K
Find the moment of inertia of a washer
Replies
4
Views
4K
Rotating Rod in Plane: Kinetic Energy & Moment of Inertia
Replies
16
Views
2K
Moment of inertia of a system of masses
Replies
10
Views
2K
Finding moment of inertia of cone
Replies
4
Views
2K
Quick question about moment of inertia
Replies
21
Views
2K
Moment of inertia of a meter stick
Replies
9
Views
6K

Hot Threads

Recent Insights

Back
Top