Moment of Inertia confusion

In summary, the problem involves calculating the moment of inertia of a system consisting of small blocks clamped at the ends and center of a rod. The axis of rotation is perpendicular to the rod and passes through a point one-fourth of the length from one end. The formula for moment of inertia is I = Mr^2 and drawing a diagram can help visualize the problem.
  • #1
K.QMUL
54
0

Homework Statement



Small blocks, each with mass m, are clamped at the ends and at the center of a rod of length L and negligible mass

Compute the moment of inertia of the system about an axis perpendicular to the rod and passing through a point one-fourth of the length from one end.

Homework Equations



I = Mr2

What I am having difficulty with

I don't understand where this axis is, it would help if someone would explain or better draw a diagram to help me understand.
 
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  • #2
K.QMUL said:
I don't understand where this axis is, it would help if someone would explain or better draw a diagram to help me understand.
Did you try drawing a diagram for yourself? The directions seem pretty straightforward.

Draw a line representing the rod. Now draw a line perpendicular to it. If it that perpendicular line were in the middle of the rod, it would be 1/2 the length from one end. Move it so that it's 1/4 the length from one end.
 
  • #3
Do you agree that one-fourth of the rod length, as measured from one end, must be midway between that end and the center point?
 
  • #4
Sorry, i figured it out before everyones reply, so I am all good. Thanks for the help though
 
  • #5


The axis in question is a line that is perpendicular to the rod and passes through a specific point on the rod. In this case, the point is located one-fourth of the length from one end of the rod. This means that the axis is not located at the ends of the rod, but rather somewhere in the middle.

To better understand this concept, it may be helpful to draw a diagram. Imagine a rod that is 4 units long, with the point in question located at the 1 unit mark (one-fourth of the length). The axis would be a line perpendicular to the rod and passing through this point. This axis would intersect the rod at the center (2 units) and would also be equidistant from both ends of the rod.

To calculate the moment of inertia about this axis, you would use the equation I = Mr^2, where M is the total mass of the system (in this case, the sum of the masses of all the blocks), and r is the distance from the axis to each block. In this example, the distance from the axis to each block would be 1 unit (since the blocks are located at 1 unit, 2 units, and 3 units from the axis).

I hope this helps to clarify the concept of the axis and how to calculate the moment of inertia in this scenario. It may also be helpful to consult with your instructor or classmates for further clarification.
 

1. What is moment of inertia?

Moment of inertia is a physical property of an object that measures its resistance to rotational motion. It is the rotational equivalent of mass in linear motion.

2. How is moment of inertia different from mass?

Moment of inertia and mass are different physical properties, but they are related. While mass measures an object's resistance to linear motion, moment of inertia measures its resistance to rotational motion. In other words, an object's mass affects how it moves in a straight line, while its moment of inertia affects how it rotates.

3. How is moment of inertia calculated?

The moment of inertia of an object depends on its mass, shape, and distribution of mass. It can be calculated using the formula I = ∫r^2dm, where I is the moment of inertia, r is the distance from the axis of rotation, and dm is an infinitesimal mass element.

4. Why is moment of inertia important?

Moment of inertia is important in understanding and predicting an object's rotational motion. It is used in various fields such as physics, engineering, and mechanics to design structures and machines that can withstand rotational forces and to analyze the motion of objects.

5. What are some common misconceptions about moment of inertia?

One common misconception is that moment of inertia is the same as torque. While they are related, torque is a measure of rotational force, while moment of inertia is a measure of an object's resistance to rotation. Another misconception is that moment of inertia only applies to circular motion, when in reality, it applies to all types of rotational motion.

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