Questions tagged [moment-of-inertia]
The moment of inertia, or rotational inertia, determines the torque needed for a desired angular acceleration about a rotational axis. Like inertial mass is the resistance to being linearly accelerated, the moment of inertial is the resistance to being rotationally accelerated.
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Moment of inertia of a quadrilateral [closed]
I found this problem in one of my tests.
Here's a uniform slab $OABC$. Now $\overline{CB}$ $= 10cm, \overline{AB} = 2cm, \angle B=\angle O=90^\circ,$ $\overline{OA} = \overline{OC}$. What will be the ...
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Derivation of Rotational Inertia for a uniform cylinder [closed]
I'm a high school student studying physics. I have foundational knowledge in calculus and physics, but my skills in the application of calculus are (evidently) weak. I was performing the derivation of ...
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Non-ideal pulley
In a non-ideal pulley (with friction at axle to be negligible) the tension on both side of rope is not equal because friction is present between rope and pulley, but when we write torque on the pulley ...
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Periodic orbits for the motion of a body with a fixed point (without forces)
It seems that non-obvious periodic orbits for the Euler-Poinsot problem do exist (inertial tensor with 3 different eigenvalues). But I could not find any precise reference for the validity of this ...
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Why are there two different tension forces on a continuous string in the pulley system shown?
In an ideal pulley system with massless and frictionless strings and pulleys, the tension is typically uniform throughout a continuous string, even when the system is accelerating. However, when ...
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Derivation of moment of inertia formula
According to Physics Libre texts:
We defined the moment of inertia $I$ of an object to be:
$$
I = \sum_i m_i r_i^2
$$
for all the point masses that make up the object.
Now my question is why is the ...
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Moment of inertia in rolling of a disc on a rough surface
A disc resting on a rough surface is given an impulse. The disc eventually starts pure rolling. In such a case when we apply conservation of angular momentum at the point of contact of the disc with ...
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Why does the pivot need to be placed at the radius of gyration for a physical pendulum to achieve the minimum oscillation period?
I was recently solving some questions and came across an interesting problem which asked to find the time period for a rod as a physical pendulum, after solving the answer came out to be its radius of ...
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Rotational mechanics - Inertial mass vs rotational mass in context with motion, relative motion
So basically moment of inertia is kind of the apparent mass, which is due to the body being in rotational motion. While calculating translational equilibrium, we take into account inertial mass rather ...
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Confusing Angular momentum
This problem has bothered me for a long time.
In my Physics 1 course we've learned that the formula for angular momentum is $$\vec L = \vec r\times \vec p + I\vec \omega,$$
where $\vec r\times \vec p$ ...
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Required force to start moving a stationary block on rollers [closed]
Hello, I am trying to figure out how to calculate the minimum required force to start moving a stationary block that is on rollers. Everywhere I search I see the formula for rolling friction being ...
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Moment of inertia doubt about rod rotating about an axis in two different ways
Does the moment of inertia in both the cases remain same or are they different about the axis shown in figure
In left one, the rod is purely rotating about the axis but in the right one the rod is ...
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Irregularities in Moment of inertia of torus
This is NOT a question regarding the derivation of the moment of inertia of a torus, but rather an irregularity which I find in it. I am most probably wrong, but can't see where. It would be helpful ...
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Melting Ice Caps: How Does It Impact Earth's Rotation and the Length of a Day?
Melting Polar Ice Caps and Earth's Rotation.
The polar ice caps contain an estimated mass of $ m = 3 \cdot 10^{19} \, kg $. This mass contributes almost nothing to the Earth's moment of inertia since ...
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When transfoming an intertia tensor from one set of principle axes to another, why does it not change the tensor?
I have two inertia tensors for a cube, $I_1$ and $I_2$ where $I_1$ is the inertia tensor centered at the cube center with the axes perpendicular to the cube faces, and $I_2$ is also centered at the ...
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