Moment of Inertia: Definition, Formula, and Examples of Its Embodiments in Life

Moment of Inertia – For ordinary people, the term “moment of inertia” will sound foreign
and they don’t even know the exact definition.
This is only natural, because the term is
generally found in Physics disciplines where not everyone studies it.

But if you hear the name “Isaac Newton”, surely most people will immediately know that the name belongs to
someone who discovered the theory of gravity in Physics.
Well, it turns out that Isaac Newton
not only discovered the theory of gravity which is always described by coconuts falling from the tree, you
, but also created the theory of Newton’s Laws related to inertia, aka inertia.

A simple example of the occurrence of inertia, aka inertia, is a top game that is played, a roller
coaster game , and a skateboard game. So, what is the moment of inertia in the study of
What is the formula for calculating this moment of inertia? What are
some examples of the manifestation of the moment of inertia in everyday life?
So, so that
Sinaumed’s understands it, let’s immediately look at the following review!

What is Moment of Inertia?

Before understanding what the moment of inertia is, it’s better if Sinaumed’s slowly understands the
definition of inertia, aka inertia, both in terms of terms and language.

The term “inertia” comes from the Latin word “iners” which means ‘sluggish’ or ‘lazy’. In
simple terms, this inertia, aka inertia, leads to the resistance of physical objects when they resist
changes in motion.
Reporting from , this inertia can
also be interpreted as a force to hold objects that are initially still to remain still or objects that
continue to move at a constant speed.

Well, it turns out that this inertia or inertia has been mentioned by a famous philosopher, Galileo Galilei who
stated that basically all things are in a state of rest. If the object moves,
it means there is an influence coming from outside.

In short, the tendency of objects to “preserve themselves” is what is known as inertia. The
greater the inertia alias possessed by an object, then the object tends to be more difficult to accelerate
or slow down its movement.
Meanwhile, the word “moment” in the term “moment of inertia” refers
to events related to inertia or inertia around us.

Then, does this inertia or inertia have anything to do with the branch of physics? Of course
there is, especially in Newton’s First Law which was coined by Isaac Newton, the founder of the theory of
In Newton’s Law I states that ” Inertia is the basic property of an object,
that is, the object will maintain its state” .

This is a simple example, when we sit quietly in a moving car, then suddenly the driver brakes suddenly
because a cat is passing by, then our bodies will immediately be pushed forward, right?
that’s a form of inertia or inertia.

In general, the term “inertia” can also refer to ‘the amount of resistance to a change in velocity’, which
is identified as mass.
As Galileo Galilei said earlier, all objects will basically remain
stationary, unless subjected to an external force (in the sense of net force = 0) which moves at a constant
So, on that basis, it can be concluded that,

“Moment of inertia is a measure of the inertia of an object to rotate on its axis.
The magnitude of the moment of inertia depends on the shape of the object and the position
of the axis of rotation.”

The existence of this matter plays a major role in rotational dynamics, such as mass in basic dynamics,
determines the relationship between angular momentum (angular center) and angular velocity, determines the
relationship between moment of force (torque) and angular acceleration, and so on.
Since this
moment of inertia is still within the scope of physics, then of course it has a special symbol, namely
I or J .

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The Relationship Between Inertia and Mass

Does Sinaumed’s know that inertia, aka inertia, has a relationship with the mass of an object?
Yep, the amount of inertia, aka inertia, also depends on the mass of the object.
The greater the mass of the object, the greater the measure of inertia alias inertia.
Likewise, the greater the inertia value of an object, the greater the force required to stop
the object.

For example, there is a sedan and a cement mixer truck that are in the middle of a stop. To
move the two vehicles at the same speed, of course, different forces are needed so that the sedan and the
cement mixer truck can move.
If that’s the case, Sinaumed’s will surely understand
that the power to push a sedan is much less than the power to push a cement mixer truck.

The Existence of the Moment of Inertia of a Point

In the discipline of Physics, there is a term for objects that are subject to inertia, namely point objects
and rigid bodies.
The striking difference between a point object and a rigid body is the change
in the distance contained in the system.
In a point object, there are 2 types of system motion,
namely 1) Center of Mass Motion;
and 2) Relative Motion.

Reporting from , the moment of inertia of an object is influenced by its mass and
distance to the point of rotation.
That is why, the formula is actually the product of the
mass of an object particle to the square of the distance from the pivot point.
Well, the
farther the mass of the object is from the axis, the greater the moment of inertia, aka the inertia, it
will have.
In this case, the formula used is:

I = mr 2


I = moment of inertia (kg.m 2 )

m = object mass (kg)

r = distance of particle to the axis of rotation (m)

Existence of Moment of Inertia in Rigid Bodies

Generally, a rigid body is an object that does not experience any change in shape, especially after being
subjected to a rotational force.
During the rotation, the particles inside the rigid body will
move in a space that has a circular trajectory, so that their positions will be relatively fixed to one
This process also prevents rigid bodies from gaining kinetic energy when they are in
translational motion.
The reference to circular motion that occurs in a rigid body is called
the moment of inertia.

Yep, the existence of the moment of inertia is not only affected by mass and distance (as in point
objects), it is also influenced by how the object forms.
The shape of a solid spherical ring,
cylinder shape, hollow ball shape, and others also has a measurement of the moment of inertia value of each.
Even the formula is also different for each form of object.

Formula for Calculating Moment of Inertia

In general, the formula to calculate it is:

I = mr 2


I = moment of inertia (kg.m 2 )

m = object mass (kg)

r = distance of particle to the axis of rotation (m)

Moment of Inertia Formula for Rigid Bodies

Previously, it was explained that the existence of this measure of inertia is not only influenced by mass
and distance (as in point objects), it is also influenced by how the object is shaped.
Yep, the
measure of inertia in the shape of an object has its own value and the formula is different depending on how
the shape of the object is.
So, here are some formulas for calculating the moment of inertia
for rigid bodies that have various shapes.

Object Shape Axis Picture Moment of Inertia formula
Stem Center I = (1/12) ml 2
Stem End I = (⅓) ml 2
Hollow Ball through diameters I = (⅔) m. r 2
Solid Ball through diameters I = (⅖) m. R 2
Solid Cylinder Cylinder axis I = (½) m. R 2
Cylinder Tube Tube axis I = (½) m. (R1 2 + R2 2 )
Thin Stem through diameters I = (1/12) m. (a 2 + b 2 )
Thin Ring Through the center and perpendicular to the radius I = m. R 2

For these rigid bodies, there are several things that need to be considered, especially in the formula for
cylindrical rod-shaped objects, namely:

  • If spherical rigid objects are multiplied by the square of the radius, then for cylindrical rigid
    bodies multiplied by the length of the rod.
    The length of the cylinder rod has the symbol
    for the letter L with units of meters (m).
  • If the rigid objects are triangular or quadrilateral, multiplied by the length of the side and the unit is
    meters (m).
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Example of a moment of inertia problem

  1. An object rotates with a radius of 0.5 m around its center and the mass of the object is 10 kg.
    So, what is the moment of inertia of the object?


Given: m = 10 kg; r = 0.5 km

Asked: I


⇔ I = mr 2

⇔ I = 10.0,5 2

⇔ I = 2.5

So, the moment of inertia on the object is 2.5 kg.m 2

  1. A solid ball has a radius of 0.5 m, and has a mass of 50 kg, determine the moment of inertia of the solid


Given: k = ⅖; m = 50 kg; r = 0.5m

Asked: I


⇔ I = kmr 2

⇔ I = ⅖. 50. 0.5 2

⇔ I = 20. 0.25

⇔ I = 5

So, the moment of inertia of the solid ball is 5 kg.m 2

  1. A cylindrical rod rotating through a shaft at the end has a length of 2 meters and has a mass of 9 kg.
    Determine the moment of inertia of the cylinder rod!


Is known:

k cylinder rod with shaft at end = ⅓

m = 9 kg; L=2m;

Asked: I


⇔ I = kmL 2

⇔ I = ⅓. 9. 2 2

⇔ I = 3.4

⇔ I = 12

So, the moment of inertia in the cylinder rod is 12 kg.m 2

The Embodiment of Moments of Inertia in
Everyday Life

The existence of this moment of inertia is not just theory and formula , you know , but there are
also manifestations that we often encounter in our daily life.
So, here are some examples
of the embodiment of moments of inertia that occur in everyday life.

1. The existence of satellites

Does Sinaumed’s know that the existence of a satellite moving in outer space is a manifestation of the
moment of inertia?
Yep, basically a satellite is an object that is outside the swan and
always rotates around a larger object without stopping.
Why does the satellite move around
a larger object without stopping?
That’s because there is inertial motion that makes it
move continuously in a circular manner.

2. Fruit and Leaves Falling From Trees

The second manifestation of the moment of inertia is the falling of fruit and leaves from a tree when the
limb is disturbed.
The state of the tree branch when it has not been shaken, will definitely be
Then, when the tree branch is shaken, it will start to move and affect the fruit and
leaves which were originally in a still state.
After that, the fruit and leaves will fall from
the tree.

3. Dust On The Carpet

The manifestation of the third moment of inertia is the dust that falls from the carpet while it is being
When you want to clean the carpet, surely Sinaumed’s will hit or slash
it with a broom, right?
Well, the carpet that was initially stationary, then moved but the
dust particles were still in a state of rest, aka in the initial state of inertia.
the carpet is slashed repeatedly using a broomstick, dust particles will fall.

4. Pushed Forward When the Car Brakes Suddenly

Has Sinaumed’s ever taken public transportation, whether it’s an angkot or a bus, then the body will be
pushed forward when the driver brakes suddenly?
Well, it can also be a manifestation of the
existence of moments of inertia in everyday life.

5. Stir the Milk in the Glass

When you want to brew milk, surely Sinaumed’s will stir it first, right? So, during the
process of stirring the milk, you will definitely see that the “current” is still rotating, even though
we have stopped stirring.
Well, it can also be a manifestation of the moment of inertia
that keeps the “flow” of milk moving, even after the stirring process is complete.

6. Athletes Running Before Long Jumping

Did Sinaumed’s ever try the long jump when he was still in school? Usually, this practice
is carried out to fulfill Basic Competencies in Physical Education subjects.
So, when we
want to do a long jump, we will definitely do a running run.
Running square off where we
are asked to run as hard as possible and then stop at a certain point, then just jump into the sandbox.
The moment when we run and then stop is the embodiment of inertia.

So, that’s a review of what is the moment of inertia along with the formula and examples of its
manifestation in everyday life.
Can Sinaumed’s name examples of other manifestations
of moments of inertia?