2
votes
1answer
71 views

Cayley-Klein Parameters

I have a very simple question(I guess )to ask $$\frac{d\mathbf{m}}{dt}= \mathbf{C} \times \mathbf{m}$$ where $\mathbf{m}$ and $\mathbf{C}$ are vectors. Assume that $\mathbf{C}$ is constant over a ...
3
votes
1answer
63 views

Stability of square of masses on strings under rotation

Imagine we have a square of masses, $m$, connected by light inextensible strings, length $l$, rotating around it's centre at angular speed, $\omega$. It's easy enough to show that there must be a ...
0
votes
0answers
70 views

Torque in an accelerated frame of reference

I'm taking a mechanics course this year and are currently studying rotational motions for my finals. The book we have explains it mostly fine, but there is one question I can't seam to find an answer ...
2
votes
4answers
177 views

Rotation axis of a rigid body

I am confused about a trivial concept. Let the rotation of a rigid body, say with one point fixed, be described by the equation $\vec{x}(t)=R(t)\vec{x}(0)$, with $R(0)=I$. Then, at each instant ...
1
vote
0answers
59 views

How to check a worm and a worm gear fit? [closed]

I know the diametral pitches must match for spur gears in order for them to run together. How to check worm gear and worm? Thanks
1
vote
1answer
93 views

Landau Lifshitz energy for uniform rotation

Landau Lifshitz claim in their Mechanics book (39.11) that for a uniform rotation we have $ E = \frac{mv^2}{2} - \frac{m}{2} (\omega \times r)^2 + U,$ where the rotation is given by $v' = v + \omega ...
1
vote
1answer
316 views

Double Compound Pendulum: why use inertia about the center of mass for bottom pendulum?

I'm trying to wrap my head around the kinetic energy of a double compound pendulum, like the one shown in the Wikipedia article on double pendulums. I know for computing the kinetic energy of the ...
0
votes
1answer
262 views

Determining friction for unbalanced wheel to roll without sliding

I'm trying to model a weighted wheel rolling without slipping. I understand that friction, by virtue of being an off-center force, affects both linear and angular acceleration. So my train-of-thought ...
4
votes
4answers
499 views

If a pendulum is on a rotating table, will a torque be generated?

Here is the set up. Very simple. A flat (i.e. horizontal table, there is no gravity) and rounded table that spins on its axis (through the center of the table). A spring mass system is now put on the ...
2
votes
1answer
441 views

Euler angle: space-fixed vs body-fixed axes

I am sooo confused!! Between active and passive, intrinsic and extrinsic, vectors and basis .... Stipulate that we stick to active rotations only. Then Standard derivation of $R(\alpha, ...
2
votes
2answers
413 views

Piston movements in four stroke cycle?

I was reading about a four stroke cycle. Here's what I understood: In the first stroke, the piston starts at the top and moves down. In the second stroke, the piston moves upwards. In the third ...
1
vote
2answers
331 views

Spin angular momentum of a system of particles : Is there any energy associated with it?

Consider a system of point particles , where the mass of particle $i$ is $μ_i$ and its position vector is $\vec{r}_i$. Let $\vec{r}_\text{cm}$ is the position vector of the center of mass of the ...
1
vote
2answers
875 views

What are the expressions for rotational and translational kinetic energies of a system of point particles?

Consider a system of point particles , where the mass of particle $i$ is $\mu_i$ and its position vector is $r_i$. What are the expressions for translational kinetic energy and rotational kinetic ...
7
votes
4answers
581 views

Why does a ping pong ball change direction when I spin it on a table?

When I spin a ping pong ball on the table, it rolls forward in the opposite direction of the spin, and then eventually changes direction and rolls backward. Here's a video demonstrating the effect. ...