Moment of Inertia: Rules & Usage Guide

AI Thread Summary
The moment of inertia can be calculated using two formulas: I = ∑m r² for point masses and I = ∫ r² dm for continuous mass distributions. The first formula is applicable when dealing with discrete point masses, while the second is used for objects with mass distributed continuously. Continuous mass distributions refer to bodies where mass is spread out over a volume rather than concentrated at specific points. Understanding when to apply each formula is crucial for accurate calculations in physics. For practical examples, refer to the provided Moment of Inertia Examples.
Neon32
Messages
68
Reaction score
1
To find Moment of inertia, there are 2 rules:
I = ∑m r2
I= ∫ r2 dm

I don't know when to use the first and when to use the second rule.
 
Physics news on Phys.org
Neon32 said:
I don't know when to use the first and when to use the second rule.
The first is useful for point masses; the second, for continuous distributions of mass.
 
Doc Al said:
The first is useful for point masses; the second, for continuous distributions of mass.
what does continuous distributions of mass mean?
 

Thread '1:1 versus 2:1 Mechanical Advantage debate'

The rope is tied into the person (the load of 200 pounds) and the rope goes up from the person to a fixed pulley and back down to his hands. He hauls the rope to suspend himself in the air. What is the mechanical advantage of the system? The person will indeed only have to lift half of his body weight (roughly 100 pounds) because he now lessened the load by that same amount. This APPEARS to be a 2:1 because he can hold himself with half the force, but my question is: is that mechanical...
View full post »

Thread 'Newton's first law?'

Some physics textbook writer told me that Newton's first law applies only on bodies that feel no interactions at all. He said that if a body is on rest or moves in constant velocity, there is no external force acting on it. But I have heard another form of the law that says the net force acting on a body must be zero. This means there is interactions involved after all. So which one is correct?
View full post »
Thread 'Beam on an inclined plane'

Thread 'Beam on an inclined plane'

Hello! I have a question regarding a beam on an inclined plane. I was considering a beam resting on two supports attached to an inclined plane. I was almost sure that the lower support must be more loaded. My imagination about this problem is shown in the picture below. Here is how I wrote the condition of equilibrium forces: $$ \begin{cases} F_{g\parallel}=F_{t1}+F_{t2}, \\ F_{g\perp}=F_{r1}+F_{r2} \end{cases}. $$ On the other hand...
View full post »

Similar threads

I How to find moment of inertia of an insect?
Replies
5
Views
922
I Moment of inertia of human body with limbs at an angle
Replies
12
Views
2K
I Resolve moment of inertia at an angle
Replies
2
Views
2K
I Moment of Inertia about an axis and Torque about a point
Replies
5
Views
3K
B Moment of Inertia of Rectangles
Replies
3
Views
3K
I Importance of Moment of Inertia for designing helicopters and propellers?
Replies
2
Views
1K
How can I calculate the moment of inertia of any object?
Replies
10
Views
2K
I Calculating Mass Inertia Product - Examples 1 & 2
Replies
2
Views
2K
Why Do Different Objects Share Similar Moments of Inertia?
Replies
1
Views
1K
I Inertia of body moving about two distinct parallel axes
Replies
10
Views
2K

Hot Threads

Recent Insights

Back
Top