# Tag Info

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### When two systems of forces acting on a rigid body are equivalent?

The equations of motion can be thought of given a specified motion, provided by the translation acceleration vector of the center of mass $\boldsymbol{a}_C$ and the rotation acceleration vector of the ...
• 2,552

### When two systems of forces acting on a rigid body are equivalent?

A theorem for a rigid body is: "Every system of forces is equivalent to a single force through an arbitrary point, plus a couple (either or both of which may be zero.)". A couple is defined ...
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### Does an irregular rigid body can only rotate in three directions?

A general rigid body has 3 principal axis. Suppose $I_1<I_2<I_3$. If it rotates around $I_1$ or $I_3$ without external torques, the angular velocity doesn't change and is parallel to the angular ...
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### Does an irregular rigid body can only rotate in three directions?

You state "an irregular rigid body has only 3 axes such that $\vec{L}_{cm}$ and $\vec{\omega}$ are parallel." I presume you mean the principal axes? In terms of the Cartesian principal ...
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### Moment of Inertia of a solid hemisphere. What am I doing wrong?

Your symmetry argument is correct, this is because say we have full sphere and an axis passing through its center. Breaking it into 2 symmetrical hemispheres means each carries half of the total ...
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### What is the angular momentum of a particle rotating around an axis in 3D?

The definition $\vec{L}_i = m \vec{r}_i \times \vec{v}_i$ is the correct one. Note that this vector will not lie along $\hat{n}$, and that's as it should be! Your derivation above makes the mistake ...
I think I found a simpler way. First you prove $(\sum_i{\tau_i})\Delta\theta$ is the change in total kinetic energy for a small $\Delta\theta$. You know the change in a single particle's kinetic ...