Inertia of System: Find w/ Pink Dot & Diagonals

In summary, the conversation discusses finding the inertia of a system where the axis of rotation passes through the center of mass. The formula for inertia is given as 4(mr^2), but there is confusion over the value of r. It is clarified that r is the perpendicular distance from the mass to the axis of rotation, which is different from the distance to the center point. The conversation ends with a reminder to review definitions for clarity.
  • #1
Hanin
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Hi, in the following problem, I need to find the inertia of the system. The axis of rotation passes through the center of mass ( the pink dot). I understand that I will be equal to 4(mr^2). However, I do not understand why r= 3 (6 divided by 2) and not sqrt13 ( half of the diagonal of the rectangle).

upload_2017-12-8_20-27-53.png

 

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  • #2
Review your definitions. r is the perpendicular distance from the mass to the axis of rotation, which is that entire line through the center, not the distance from the mass to the point in the center.
 
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Likes Abhishek kumar and Hanin
  • #3
I think you were thinking rotation about the c.g. into/out of page.
 

1. What is inertia of system?

Inertia of system refers to the tendency of a system to resist changes in its state of motion. It is a property of matter that causes objects to maintain their current state of motion unless acted upon by an external force.

2. How is inertia of system measured?

The inertia of a system can be measured by calculating its mass and the acceleration needed to change its state of motion. The greater the mass and acceleration, the greater the inertia of the system.

3. What is the importance of finding inertia of system with a pink dot and diagonals?

Finding the inertia of a system with a pink dot and diagonals can help determine the distribution of mass within the system. By analyzing the motion of the pink dot and diagonals, we can gather information about the system's mass distribution and its tendency to resist changes in motion.

4. How does inertia of system affect everyday life?

Inertia of system plays a significant role in our everyday lives. It is the reason why objects remain stationary or continue moving unless acted upon by a force. It also explains why we feel a force pushing us back when a car suddenly accelerates or stops.

5. Can inertia of system be changed?

Inertia of system is a property of matter and cannot be changed. However, the state of motion of a system can be altered by applying external forces. This means that the inertia of a system remains constant, but its motion can be changed by external influences.

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