A rigid body is an object that does not change shape when subjected to an external force. If an object seems to rotate through an axis, how do we calculate its moment of inertia.
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00:00Here are skinny sticks or sticks that have a much greater length compared to their thickness.
00:08The real object of the skinny stick is the wire.
00:14The length of the skinny stick is L.
00:20Suppose the skinny stick is on a two-dimensional surface.
00:26There is a shaft located at a distance d from one end of the stick.
00:30This axis is none other than the z-axis.
00:35That is to say, the stick rotates horizontally.
00:42Based on the concept of moment of inertia, a point particle with mass m and located at a distance r from the axis has a moment of inertia of m r-squared.
00:51How do we determine the r-value in this case?
00:53Is the distance from the shaft to the nearest tip of the stick or d?
01:06Is the distance from the shaft to the middle of the sticks or d plus half L?
01:14Or is the distance from the shaft to the furthest end of the sticks or d plus L?
01:18Which of these three possibilities is true or none of them?
01:26From here, we will get to know the distance dilemma.
01:36Now, suppose that at a distance r from the axis, there are three objects with the same mass but different shapes.
01:45There is a cube.
01:49A sphere.
01:53And a polyhedron.
01:58If these objects rotate, will they all have the same value of moment of inertia?
02:05From here, we will face a form dilemma.
02:12These two types of dilemma will always arise if an object whose mass is continuously distributed rotates about a certain axis.
02:19To get the moment of inertia of an object like this, we can use at least two methods.
02:27The first is the Riemann sum.
02:30The second is integral.
02:34We will discuss this in the next tutorial.
02:39Hopefully this is useful and don't forget to watch the next video.