Finding the Moment of Inertia of a System

In summary, moment of inertia is a physical property that quantifies an object's resistance to changes in its rotational motion. It is important in the design and analysis of systems and can be calculated by summing the products of mass and distance squared or using mathematical equations for specific shapes. The moment of inertia is affected by the mass and distribution of mass of the system and cannot be negative as it represents the resistance to change in rotational motion.
  • #1
Jacob87411
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1
Rigid rods of negligible mass lying along the y-axis connect three particles (Fig. P10.20). The system rotates about the x-axis with an angular speed of 1.20 rad/s.

(a) Find the moment of inertia about the x axis.

So isn't the moment of inertia given by the sum of mr so..

(4kg)(3m)+(2kg)(-2m)+(3kg)(-4m) = -4?
 

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  • #2
That should be the sum of [itex]m r^2[/itex].
 
  • #3
so (4)(3^2)+(2)(-2^2)+(3)(-4^2) = (4)(9)+(2)(4)+(3)(16)=36+8+48=92?
 
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  • #4
Yes, in units of kg-m^2.

(Realize that r is the distance from the axis, so it should be positive.)
 
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What is moment of inertia?

Moment of inertia is a physical property that measures the tendency of an object to resist changes in its rotational motion. It is dependent on the mass and distribution of mass of an object.

Why is it important to find the moment of inertia of a system?

The moment of inertia helps us understand how an object will rotate in response to an external force. It is crucial in the design and analysis of systems such as cars, airplanes, and satellites.

How do you calculate the moment of inertia of a system?

The moment of inertia can be calculated by summing up the products of mass and distance squared for each individual component of the system. Alternatively, it can also be calculated using mathematical equations for specific shapes such as spheres, cylinders, and rods.

What factors affect the moment of inertia of a system?

The moment of inertia is affected by the mass and distribution of mass of the system. Objects with more mass and mass concentrated farther from the axis of rotation will have a larger moment of inertia.

Can the moment of inertia of a system be negative?

No, the moment of inertia is always a positive value because it represents the resistance to change in rotational motion. A negative moment of inertia would imply that the system would accelerate without an external force, which is not physically possible.

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