All Questions
7
questions
0
votes
2
answers
115
views
When to apply $I_c \underline{\omega} = \underline{M_c}$?
I was solving an exercise the other day, about a rolling cylinder on an inclined plane. Initially the cylinder slides, but then it begins to roll and the problem wanted to know the velocity of the ...
- 402
2
votes
1
answer
1k
views
Angular velocity across different reference frames
In classical mechanics:
Logically, it appears to me that if I draw a mark on a ball and let it roll, the amount of time that will pass before the mark reaches the same position (in terms of angles: ...
- 183
2
votes
1
answer
330
views
Understanding Euler's Rotation equation for rigid bodies (Frames Of Reference)
$$
\tau_b=I_n\dot\omega_b+\omega_b\times I_b\omega_b
$$
Now in the above is Euler's famous rigid body rotation equation, in the body frame of reference ..... this does not make sense to me. How can a ...
3
votes
1
answer
1k
views
Why is total kinetic energy always equal to the sum of rotational and translational kinetic energies?
My derivation is as follows.
The total KE, $T_r$ for a rigid object purely rotating about an axis with angular velocity $\bf{ω}$ and with the $i$th particle rotating with velocity $ \textbf{v}_{(rot)...
user86425
0
votes
1
answer
332
views
Lagrangian of a Heavy Symmetrical Top - Inertial or Non-inertial Frame?
I'm having some confusion with the analysis of a symmetrical top (specifically, a heavy top, but this is not very important for the question).
Following Landau and Lifshitz's Mechanics, on page 110 ...
- 3
3
votes
1
answer
137
views
These components of the angular velocity are given in what reference frame?
When we have a rigid body, the rigidity constraint allows us to write the trajectory $\mathbf{r}_i$ of the $i$-th particle as
$$\mathbf{r}_i(t) = R(t)\mathbf{b}_i + \mathbf{w}(t),$$
where we are ...
- 36.4k
3
votes
0
answers
130
views
Gauge formalism in rigid body mechanics
When doing calculations in rigid body mechanics, it is necessary to choose an origin to calculate torques and angular momenta. However, the underlying dynamics does not depend upon the choice of that ...
user17116