Tagged Questions
0
votes
1answer
42 views
Calculating the moment inertia for a circle with a point mass on its perimeter
I want to calculate the tensor of the moment of inertia. Consider this situation:
The dot represents a points mass, in size equal to $\frac{5}{4}m$. $m$ is the mass of the homogenous circle. I'm ...
1
vote
1answer
76 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 ...
-1
votes
1answer
90 views
Confusions about rotational dynamics and centripetal force
I am a high school student. I am having confusions about the centripetal force and rotational motion . I have known that a body will be in rest or in uniform velocity if any force is not applied. But ...
3
votes
2answers
135 views
what's the physical significance of the off-diagonal element in the matrix of moment of inertia
In classical mechanics about rotation of rigid object, the general problem is to study the rotation on a given axis so we need to figure out the moment of inertia around some axes. In 3-dimensional ...
4
votes
4answers
140 views
Wheel locks and spinout
Imagine driving in a straight line on a ice lake, when you hit the brakes, if your goal is to stay in straight path with no spinout, which wheels would you choose to have locked: front or rear? ...
2
votes
2answers
158 views
Foucault pendulum
The equations of motions for a Foucault pendulum are given by:
$$\ddot{x} = 2\omega \sin\lambda \dot{y} - \frac{g}{L}x,$$
$$\ddot{y} = -2\omega \sin\lambda \dot{x} - \frac{g}{L}y.$$
What are the ...
1
vote
0answers
59 views
Limitations on the choice of axis of rotation regarding rolling wheels
Consider a situation where a wheel is rolling without friction on a level surface. Call the center of the wheel $C$, the point where the wheel contacts the ground $G$, and some arbitrary other point ...
0
votes
3answers
261 views
Aircraft Level Flight Trajectory
An aircraft climbs to 15000 feet and enters 'level flight' phase. My basic knowledge of physics says that forces on the aircraft at this time are balanced - as seen in this diagram.
...
0
votes
1answer
85 views
What happens at the end of Coriolis Deflection
Consider we launch a cannonball due south from a point at 45 degrees latitude in the Northern Hemisphere (e.g the point defined with the co-ordinate system on this diagram). The cannonball travels for ...
2
votes
1answer
237 views
Why is an electric motor more efficient at higher loads?
My question is driven by the plot below. We see that acceptable operating range of a motor is between 50-100% of the rated load. Below 40% or so the efficiency of the motor drops off dramatically.
...
0
votes
2answers
249 views
Precession of angular velocity about the body-fixed axis
My textbook mentions that under force-free motion of a symmetric top, its angular velocity vector $\overrightarrow \omega$ precesses about the $z$-axis of the body-fixed coordinate system. This seems ...
8
votes
2answers
616 views
Hamiltonian is conserved, but is not the total mechanical energy
I wondering about the interpretation for the energy difference between the Hamiltonian and the total mechanical energy for systems where the Hamiltonian is conserved, but it is not equal to the total ...
3
votes
1answer
274 views
Rotating/Translating Disk
I was trying to understand an aspect of rotational dynamics and thought of a problem to help me learn. I'm sure this problem has been considered by countless people in the past, but I'm having some ...
5
votes
1answer
114 views
Elementary derivation of the motion equations for an inverted pendulum on a cart
Consider a cart of mass $M$ constrained to move on the horizontal axis. A massless rod is attached to the midpoint of the cart, having a mass $m$ on its endpoint. See wikipedia for a picture and for a ...
8
votes
1answer
281 views
Why does a cuboid spin stably around two axes but not the third?
Let $C$ be a cuboid (rectangular parallelepiped) with edges of lengths $a < b < c$.
Consider an axis that passes through the centers of two opposite faces of $C$. There are three such axes, ...
0
votes
0answers
99 views
Assume a spool rolls down a slope with its body (not its ends) in contact with the slope
I was doing a little mental exercise and imagined the above scenario. I can intuitively see that in the described case, the smaller the diameter of the spool body, the larger the proportion of the ...
2
votes
2answers
163 views
Ideal 2D Unicycle Kinematics
A particle is connected to a massive wheel by a rigid rod. The wheel can roll without slipping on a horizontal surface. The particle is free to rotate around the centre of the wheel.
I believe the ...
2
votes
2answers
456 views
Meaning of angular velocity in a rotating system
When you study the motion of a rigid body you have $\vec\omega$, the vector associated to angular velocity. In the case you are using Euler angles and want a quick formula for the rotational kinetic ...
1
vote
1answer
162 views
Determining axis of rotation from angular speeds about axes
I think my pure-math head is messing with me on the question below: my physics and CS friends both seemed to think it was a simple computational thing, and my program says the method works, but now ...
0
votes
2answers
490 views
How to interpret this vertical circular motion problem?
A bucket of water is tied to a rope and swung in a vertical circle.
The distance from the bucket centre to the axis of rotation is
$2.08m$. Calculate the angular velocity (in $rad s^{-1}$) of ...
1
vote
1answer
263 views
What techniques can be used to analyze a rod rotating about the edge of a table?
A uniform rod of length $4x$ is rotating
about the edge $O$ of the table. (The rod does not fall off the table.) The centre of mass $G$ of the rod is distance $x$ away from $O$. The rod is making ...
2
votes
1answer
417 views
Normal force in a compound pendulum (physical pundulum) system?
Consider a compound pendulum pivoted about a fixed horizontal axis, illustrated by the force diagram on the right:
#
Okay, I can't figure out where the normal force on the pendlum should point ...
2
votes
2answers
203 views
What sustains a rigid body's rotation at its constant angular(rotational) speed?
Continuing from the following scenario from my previous question Centripetal force of a rotating rigid body? :
Consider someone pushing a roundabout in a playground. Initially the
roundabout is ...
4
votes
1answer
206 views
How do I visualize the non-coaxial rotation of this device?
The picture below shows an isolated system with a fairly massive wheel at one end, attached via its axle to a long shaft, like a bike tire on a bike frame, but the bike frame is merely a low mass ...
1
vote
3answers
2k views
Factors affecting torque and RPM of a motor
I'm not a physics guy, not even basic concept of a DC motor is easy for me. My question is, how these parts of a motor affects it's RPM and Torque? I had my research a while ago so I filled out some, ...
2
votes
0answers
540 views
Forces and torques about the CENTER OF MASS of a physical pendulum
I'm currently stumped by the following situation. Say we've got a rectangular physical pendulum (think ruler with a hole-punch at one end).
It's trivial to analyze the motion of the pendulum with the ...
-1
votes
1answer
95 views
How to find replacement function of a mass?
I wonder how I can find the replacement function of the center of the blue mass? The center of mass of the blue mass is $(0,0)$ and the blue mass is homogeneous. The masses do not move at t=0 in the ...
0
votes
1answer
178 views
Angular velocity $\omega$ by $v$
We have two girls, with mass (M). They become close to each other in speed of V. The distance between them is 3L.
I was asked to calclute the Angular velocity (w) of the two girls. So I set the ...
2
votes
0answers
147 views
Why do control moment gyroscopes exhibit “torque amplification”?
There are a number of articles that describe the benefits of using control moment gyroscopes (CMGs) over reaction wheels in inertial navigation applications. One of the primary benefits of using a CMG ...
2
votes
3answers
223 views
how to represent the effect of linking rigid-bodies together?
I have 2 rigid-bodies (b1,b2) if i linked one to the other (as if they are conjoined together) , how to represent b1 effect on b2 and b2 effect on b1
Is there any LAW that affect the ...
1
vote
1answer
225 views
Problem based on Rotational Motion [closed]
A spool of mass $\mathsf m$ and inner radius $\mathsf r$ and outer radius $\mathsf{2r}$, having moment of inertia $\Large\mathsf{\frac{mr^2}{2}}$ is made to roll without sliding on a rough ...
1
vote
2answers
214 views
Why do balls in a spinning ellipsoid move to the minor axis plane?
There is a question concerning the Physics of a small child's tall that has been bothering me for some time now. I have investigated this to a small degree, but I have not been able to find a ...
19
votes
1answer
988 views
Why does this object periodically turn itself?
See this video about 30 sec in. http://www.youtube.com/watch?v=dL6Pt1O_gSE
Is this a real effect? Why does it seem to turn periodically?
Can it be explained by classical mechanics alone?
Is there a ...
5
votes
1answer
855 views
Why are infinitesimal rotations commutative, whereas finite rotations are not?
Infinitesimal rotations commute and every finite rotation is the composition of infinitesimal rotations which should logically mean they also commute; but they don't. Why?
2
votes
1answer
391 views
Lean angle of a turning bicycle
I'm asked to derive a relationship for the leaning angle of a bicycle with the following specs:
Center of gravity for bike and rider is a distance $L$ above the ground when vertical, and the total ...
1
vote
1answer
133 views
Is it theoretically possible for the orientation angle of a projectile to remain exactly equal to the orientation of velocity?
This question is sparked by my answer to this question: Is this simulation following real physics?
After examining the math, I don't see how it is theoretically possible for the situation simulated ...
1
vote
1answer
209 views
Artificial Gravity - Spinning Station Questions II
In an answer to Artificial Gravity - Spinning Station Questions Vintage wrote:
A theoretical space station of radius 900 meters, doing a complete rotation every 60 seconds (in order to generate ...
28
votes
4answers
3k views
How can earthquakes shift the earth's axis?
One often comes across news articles that claim that an earthquake shifted the earth's axis.
http://news.google.com/?q=earthquake%20shifted%20OR%20shifts%20earth%27s%20axis
If you ignore the ...
2
votes
3answers
470 views
How long for a frictionless top to fall over?
We've previously discussed why it is that spinning tops do not fall over, see: Why don't spinning tops fall over?
However, as the highest rated answer notes, the angular momentum of the spinning top ...
3
votes
3answers
797 views
Could life survive a pole shift caused by an asteroid collision?
Could life on earth survive a large pole shift caused by an asteroid collision?
I became aware that there are people who believe that the earth's pole suddenly shifts. That is, its rotational ...
6
votes
7answers
1k views
Why does a car engine not do work if the wheels don't slip?
I saw this mind boggling result that if the tires don't slip then the work done by an engine to move a car is zero. Why is this true? Moreover, what does this truly mean?
Update: Sorry about not ...
1
vote
1answer
598 views
Relation of angular speed of a rigid body to Euler's Angles
My Question was like this and i have realised few things and still have some doubts
I have a book in which a paragraph goes like this
Now, $\dot\phi$, $\dot \theta$,
$\dot\psi$ are respectively ...
10
votes
3answers
503 views
Which direction will Coriolis forces deflect a bubble?
If I throw a ball straight up, it deflects slightly to the west due to Coriolis forces. If instead I watch a bubble float up in water, is the bubble deflected west, east, or neither?
I think the ...
3
votes
2answers
560 views
Question about moment of inertia and velocity
First off, I swear this is not homework. I'm doing some practice problems because I got an exam coming up. I'm stuck on this one:
I figured I would use energy conservation for this problem. So since ...
