# Moment of Inertia Concept

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The moment of inertia can be defined as a measure of an object's ability to maintain its angular speed of rotation. A measure of how difficult it is for a stationary object to rotate. A measure of how difficult it is for a rotating object to stand still. or a measure of how difficult it is for an object to change from one angular velocity to another.

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00:00On the left, there is a wooden ball connected to a 60 cm long rope.

00:07On the right, there is a steel ball of the same diameter and the same string.

00:17You can practice this, or just imagine it.

00:20Imagine your palm holding the end of the string that is not connected to the ball.

00:27Then you move your hand to spin the ball.

00:31Your palm will be the axis of rotation of the ball.

00:36The ball that was previously stationary will spin at a rate of 2 revolutions per second, or 4 pi radians per second.

00:45Which of the two systems is the most difficult to spin, or the most difficult to achieve the desired speed?

00:54Of course, wooden balls are easier to achieve the desired speed.

00:59Our arms feel light to do that, and don't feel sore.

01:06This is different from steel balls.

01:09To reach that speed, our arms will feel sore.

01:16Here, the lengths of the ropes are the same.

01:19The diameter of the ball is also the same.

01:22The only difference is the mass.

01:26In other words, the difficulty of an object to rotate is proportional to the mass of the object.

01:39In the second experiment, we will use wooden balls and different lengths of rope.

01:45On the left, the length of the rope is 30 cm.

01:49On the right, the length of the rope is 120 cm.

01:56We want to spin the ball from rest until it reaches a speed of 2 revolutions per second, or 4 pi radians per second.

02:04Which of these two systems is the most difficult to achieve the specified speed?

02:11It turns out that a rope with a shorter radius is easier to reach that speed.

02:18At a large radius, it will be difficult for us to rotate it.

02:22Our arm requires more energy.

02:28Two different systems with the same object mass, and the same object size, but different rotation radii.

02:37In other words, the difficulty of an object to rotate is proportional to the radius of rotation.

02:44From here, we know the term moment of inertia.

02:54The moment of inertia can be defined as a measure of an object's ability to maintain its angular speed of rotation.

03:01A measure of how difficult it is for a stationary object to rotate.

03:05A measure of how difficult it is for a rotating object to stand still.

03:09Or a measure of how difficult it is for an object to change from one angular velocity to another.

03:18Thank you for watching this video.

03:20And, don't forget to watch the next video.