All Questions
22 questions
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Absolute Angular Velocity - How to use?
From my dynamics course, we were introduced to the so-called absolute angular velocity of a rigid body. Below is a short diagram:
The following equation for the velocity of point P on a rigid body is ...
- 31
3
votes
1
answer
302
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Relation between "method of moving frames", spin connection, Cartan forms, and classic rotational kinematics in $\mathbb{E}^n$
I want to know how the "method of moving frames" involving things like connection 1-forms, torsion 2-forms, spin connections, etc. are applied to basic rotational kinematics in flat 3-space (...
- 477
1
vote
1
answer
60
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Conceptual difficulty with with component accelerations in polar coordinates
In kinematics why is the acceleration along the radius not the time derivative of the velocity along that radius?
0
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1
answer
110
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Trajectory of particle thrown from the center of rotating frame of reference
So we have a rotating platform with two frames o reference: the one which is static, $O:\{x,y,z\}$, and the one wich is rotating along the platform, $O':\{x',y',z'\}\ (z\equiv z')$. The platform is ...
- 420
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2
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434
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Integrating Angular Velocity Vector using Rodrigues' Rotation Formula
My understanding is that Rodrigues Rotation Formula can be used to explicitly compute an exact rotation associated with a constant angular velocity vector over a given time step.
How do you derive the ...
- 982
3
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1
answer
242
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Kinematics of a rolling disk on a static disk (variation of the Euler disk)
I'm puzzled by the following problem. Consider a simple tilted disk $\mathcal{D}$ of radius 1 (in any unit) rolling without sliding on top of a static horizontal disk $\mathcal{S}$. The normal $\...
- 7,677
4
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1
answer
2k
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Kinematics of a 3-wheeled omnidirectional robot
Consider a 3-wheeled, omnidirectional robot (also called a kiwi drive). To see what this looks like see this YouTube video. We can control the motor speeds using a microcontroller.
Task: We have to ...
- 1,325
0
votes
2
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465
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Angular velocity to linear velocity Modern Robotics textbook
In the second to last sentence, I have no idea how $v = (2,0)$ was calculated. Can someone derive this for me in detail, or with a picture?
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-2
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1
answer
87
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Why does the radius of curvature is constant in $n$-$t$ coordinate kinematics?
Deriving the relations kinematics on an $n$-$t$ coordinate system is said that if we have a particle $A$,after differential of time $dt$ the particle moves to $A'$. Assuming a curvilinear motion, the ...
0
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1
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375
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Angular acceleration of ball when falling [duplicate]
Why is it assumed that angular acceleration is 0 when a ball is midair after rolling off a surface with constant velocity?
5
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4
answers
229
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Is this a kinematics paradox?
You consider a shaft which can rotate freely (there will be of course a frame with ball bearing to hold the shaft firm and to allow it to rotate with low friction); fixed on this shaft there are two ...
- 768
1
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1
answer
153
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Finding The Trajectory of particle Kept on a rotating surface
Suppose we "Keep" a particle on a circular, rotating turn-table, rotating with constant angular velocity $\dot{\theta}$, (i.e, the at $t=0$,when the particle makes contact with the table, the ...
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2
votes
1
answer
128
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Does mass matter at all for kinematics vertical questions w/o friction?
This is the specific question w/o information on mass given, I think here is not enough info.
A block and a sphere are each released from rest at the top of an incline from the same height. The ...
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1
vote
2
answers
1k
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Relative velocities in Circular Motion
Recently I saw the following interesting problem
Ann is sitting on the edge of a carousel that has a radius of 6 m and is rotating steadily. Bob is standing still on the ground at a point that is ...
- 199
1
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0
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86
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Computing angular acceleration of a composition of coordinate frame transformations
Given two coordinate frames $A$ and $B$, we can define the transformation between them by:
$[\vec r_{AB}]_A$, the vector from the origin of $A$ to the origin of $B$ (resolved in frame $A$), and
$q_{...
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2
answers
1k
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How to show angle between velocity and acceleration vector is constant in polar co-ordinates? [closed]
In polar co-ordinates we have
$\vec{r} = r\hat{r}$ and
$\vec{v} = \dot{r}\hat{r} + r\dot{\theta}\hat{\theta}$ and
$\vec{a} = (\ddot{r}-r\dot{\theta}^2)\hat{r} + 2\dot{r}\dot{\theta}\hat{\theta}$
...
- 293
3
votes
1
answer
746
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What precisely does an angular accelerometer measure and how can one obtain an SO(3) Rotation from said measurements?
tl;dr
If one has an angular accelerometer, what is the motion that it actually measures?
If we have a perfect (i.e. noise-free, error-free, perfectly aligned, ...) 3-axis angular accelerometer, ...
- 191
3
votes
2
answers
254
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In Uniform Circular Motion, why does the normal accelaration not increase the magnitude of velocity?
This very simple question was posed by a high-school student in the class.
Consider a particle going in a uniform circular motion (uniform implies that the speed is constant). We know that there is a ...
- 661
0
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1
answer
1k
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Deriving some uniform circular motion equations
My question basically boils down to this. How do we derive these relationships.
1.)What is the relationship between radius and centripetal force? (inverse, but why?)
2.)What is the relationship ...
-3
votes
2
answers
864
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Why the bob leaves the circular path when tension in the string becomes zero [duplicate]
In vertical circular motion of a bob attached with a string, we say that the bob leaves the circular path when tension in the string becomes zero.
But even when tension becomes zero there's always a ...
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2
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2
answers
954
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What is the percentage of energy recovery in Kinetic Energy Recovery Systems(KERS) in cars?
Kinetic Energy Recovery Systems (KERS) use flywheels to recover energy from the kinetic motion of cars. They use a rotating flywheel that generates energy as it rotates- this generates the electric ...
- 303
8
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4
answers
3k
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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.
...
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