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harpazo
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In simple terms, what exactly is meant by moment of inertia as taught in Calculus 3?
MarkFL said:Simply put, it is the torque needed for a desired angular acceleration about a rotational axis. :D
I will post three questions tomorrow that involve p = another variable in relation to the Center of Mass and Moments of Inertia and Radius of Gyration.MarkFL said:Here is a better explanation sent to me via PM (I simply copy-pasted from Wikipedia):
Moment of inertia, $I$, is not a torque, rather it is the resistance an object has to a change in its state of rotational motion, i.e.
$\alpha = \dfrac{\tau_{net}}{I}$
... mass is its counterpart in the translational world.
Moment of inertia is a physical property of an object that describes its resistance to rotational motion. It is a measure of how difficult it is to change an object's rotational velocity.
Moment of inertia is calculated by multiplying the mass of an object by the square of its distance from the axis of rotation. This is often represented by the equation I = mr², where I is moment of inertia, m is mass, and r is distance from the axis.
The moment of inertia of an object directly affects its rotational velocity. Objects with a higher moment of inertia will have a lower rotational velocity, while objects with a lower moment of inertia will have a higher rotational velocity.
The shape of an object plays a significant role in determining its moment of inertia. Objects with most of their mass concentrated towards the axis of rotation will have a lower moment of inertia, while objects with their mass distributed further from the axis will have a higher moment of inertia.
Moment of inertia is an important concept in fields such as engineering, physics, and mechanics. It is used to calculate the stability and performance of rotating objects, such as motors, turbines, and flywheels. It is also crucial in understanding the behavior of objects in space, such as planets and satellites, and in sports like figure skating and gymnastics.