How is the moment of inertia related to the square of the distance?

AI Thread Summary
The moment of inertia (I) is defined by the equation I = MR², indicating that it is directly proportional to both mass (M) and the square of the distance (R) from the axis of rotation. An increase in mass results in greater inertia, while a decrease leads to less inertia, provided the distance remains constant. The relationship to the square of the distance arises because the torque needed to achieve a certain rotational acceleration increases with the distance of the mass from the axis. This means that the further the mass is from the axis, the more difficult it is to rotate the object. Understanding this relationship is crucial for analyzing rotational dynamics.
Hardik Batra
Messages
130
Reaction score
5
Moment of inertia is
I = MR2
object has more mass means more inertia and less mass means less inertia.
That means moment of inertia is directly proportional to mass.
But how the moment of inertia is directly proportional to the square of the distance.?
 
Physics news on Phys.org
Hardik Batra said:
Moment of inertia is
I = MR2
For a point mass, not in general.

Hardik Batra said:
object has more mass means more inertia and less mass means less inertia.
OK.

Hardik Batra said:
That means moment of inertia is directly proportional to mass.
Only if the distance to the axis--the R--is fixed.

Hardik Batra said:
But how the moment of inertia is directly proportional to the square of the distance.?
It's a measure of the torque required to produce a given rotational acceleration. Loosely: The further the mass is from the axis, the harder it is to get it to rotate.
 
but why it is square of the distance rather than only distance.
 
Thanks. It helpful for me.
 

Thread 'Is calling fictitious forces "not real" just about terminology?'

Hi there, im studying nanoscience at the university in Basel. Today I looked at the topic of intertial and non-inertial reference frames and the existence of fictitious forces. I understand that you call forces real in physics if they appear in interplay. Meaning that a force is real when there is the "actio" partner to the "reactio" partner. If this condition is not satisfied the force is not real. I also understand that if you specifically look at non-inertial reference frames you can...
View full post »

Thread 'Derivation of Hamilton's Principle: Questions'

I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
View full post »

Similar threads

I How to find moment of inertia of an insect?
Replies
5
Views
961
I Resolve moment of inertia at an angle
Replies
2
Views
2K
I Explanation of parallel axis theorem
Replies
2
Views
1K
I Moment of Inertia about an axis and Torque about a point
Replies
5
Views
3K
I Calculating Mass Inertia Product - Examples 1 & 2
Replies
2
Views
2K
I Importance of Moment of Inertia for designing helicopters and propellers?
Replies
2
Views
1K
I Moment of inertia of human body with limbs at an angle
Replies
12
Views
2K
B Why does torque increase with increasing moment of inertia?
Replies
13
Views
2K
How can I calculate the moment of inertia of any object?
Replies
10
Views
2K
Why Do Different Objects Share Similar Moments of Inertia?
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top