How Do You Calculate the Moment of Inertia for a Uniform Solid Block?

AI Thread Summary
To calculate the moment of inertia for a uniform solid block with mass 0.172 kg and dimensions 3.5 cm x 8.4 cm x 1.4 cm, the formula involves integrating r^2 dm, where r^2 is the distance from the axis of rotation. The correct substitution for dm is based on the block's density, expressed as density times dxdydz for a three-dimensional integral. For simplification, if integrating over just two dimensions, dm can be represented as height times dxdyd. Understanding these substitutions is crucial for accurately calculating the rotational inertia about the specified axis. Proper application of these principles will yield the desired moment of inertia.
demonelite123
Messages
216
Reaction score
0
a uniform solid block has mass 0.172 kg and edge lengths a=3.5cm, b=8.4cm, and c=1.4cm (c is the height of the rectangular solid).Calculate its rotational inertia about an axis through one corner and perpendicular to the large faces.

i know the formula is integral of r^2 dm, but i have no idea what to do here. i have r^2 = a^2 + b^2. but i don't know how what to substitute for dm.
 
Physics news on Phys.org
Hi demonelite123! :smile:

(try using the X2 tag just above the Reply box :wink:)
demonelite123 said:
i know the formula is integral of r^2 dm, but i have no idea what to do here. i have r^2 = a^2 + b^2. but i don't know how what to substitute for dm.

If r2 = x2 + y2, then dm = density times dxdydz (or, if you're only integrating over x and y, then dm = hdxdy). :smile:
 

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

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
Rotational inertia of square about axis perpendicular to its plane
2
Replies
52
Views
4K
Moment of inertia of a cone -- Why do we divide the equation dI = dm*r^2 by two?
Replies
6
Views
4K
How do calculate this moment of inertia?
Replies
3
Views
1K
Find the moment of inertia of a washer
Replies
4
Views
4K
Calculate the moment of inertia of this body
Replies
4
Views
1K
How to calculate the moment of inertia of a bar with two masses on it?
Replies
24
Views
4K
Calculating the moment of inertia of a solid sphere
Replies
3
Views
2K
Calculating the moment of inertia of Cone
Replies
4
Views
3K

Hot Threads

Recent Insights

Back
Top