All Questions
Tagged with kinematics classical-mechanics
255 questions
30
votes
4
answers
73k
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Difference between momentum and kinetic energy
From a mathematical point of view it seems to be clear what's the difference between momentum and $mv$ and kinetic energy $\frac{1}{2} m v^2$. Now my problem is the following: Suppose you want to ...
- 1,191
18
votes
5
answers
605
views
Does the mass point move?
There is a question regarding basic physical understanding. Assume you have a mass point (or just a ball if you like) that is constrained on a line. You know that at $t=0$ its position is $0$, i.e., $...
- 181
12
votes
2
answers
16k
views
Understanding terms Twist and Wrench
In kinematics, physics and especially robotics, we often encounter the terms Twist and Wrench. Twist is (LinearVelocity, AngularVelocity) and Wrench is (Force, Torque). The reason I'm confused is I ...
- 505
8
votes
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.
...
- 183
7
votes
4
answers
3k
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Is there a formula that gives the position of an object depending on the time, but which doesn't allow the object to surpass the speed of light?
I have found these two formulas:
$v = at + v_0$
$x = \frac{1}{2}at^2 + v_0t + x_0$
a is the acceleration
v is the velocity
x is the position
t is the time
$v_0$ is the initial velocity
$x_0$ is the ...
- 1,643
7
votes
2
answers
2k
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What is the highest energy position for a double pendulum? And for which energy positions is it chaotic?
Math/physics teachers love to break out the double pendulum as an example of chaotic motion that is very sensitive to initial conditions. I have some questions about specific properties:
For a ...
- 195
7
votes
4
answers
633
views
Speed resulting from tangentially applying force to solid spheres with different mass distributions
Given are two solid spheres of the same size and weight. They both have their center of mass at their geometric center.
One of them (A), however, has most of its ...
- 133
6
votes
2
answers
17k
views
Is a heavier skier faster? [duplicate]
Is it true that a heavier skier goes faster? If it is, why is that?
My intuition would be that the speed gained by a skier should be independent from its mass, since both its acceleration and the ...
6
votes
2
answers
3k
views
Find the minimum value of velocity [closed]
Find the minimum value of the initial velocity $u$ of the particle such that the particle crosses the wheel of radius $R$.
Details and assumptions
$R=2m$
$g=9.8m/s^2$
Neglect air resistance.
All ...
- 265
5
votes
5
answers
3k
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How does an object's motion behave if dropped from an aeroplane travelling diagonally upwards?
Imagine an aeroplane travelling with velocity $v$ at some angle $\alpha$ from East to North.
A box is dropped from the aeroplane.
What would the projectile of the box be? Would it be a parabola with ...
- 4,637
5
votes
2
answers
1k
views
The Double Integrator: Matching velocity and position as quickly as possible with only a limited amount of force available
If a body with mass $m$ begins at position $x_0$ with velocity $v_0$ and experiences a force that varies as a function of time $f(t)$ (and we ignore gravity, friction, and everything else that might ...
- 375
5
votes
4
answers
229
views
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
5
votes
2
answers
2k
views
Rigid body dynamics joints
I can't seem to find any info on connected rigid bodies by a joint. Can someone explain the basics to me? I'm trying to do a little research to find out how feasible it would be to implement 3d ...
- 151
5
votes
3
answers
3k
views
Does more rain strike a vehicle while moving or while stopped (or neither)? [duplicate]
Assume there is a rainstorm, and the rain falling over the entire subject area is perfectly, uniformly distributed. Now assume there are two identical cars in this area. One is standing still, and ...
- 251
4
votes
2
answers
576
views
Potential for chasing/pursuit problems
There are many interesting kinematics problems, where the velocity vector of one moving body points towards another moving body. For example, consider the well-known problem of a dog chasing a rabbit (...
- 377
4
votes
1
answer
780
views
Is Centripetal Velocity a Thing?
I'm quite new to physics so this question may sound dumb for many of you. But when I was learning about uniform circular motion, all sources I can find talks about centripetal acceleration, and, when ...
- 143
4
votes
3
answers
69k
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Difference b/w Kinetics & Kinematics w/concrete example
(I know whether I understand this or not doesn't matter much to my work & study but am just curious.)
I still can't differentiate in my head kinetics and kinematics (similar thread is found but ...
- 143
4
votes
2
answers
2k
views
Can these figures demonstrating the safety of "Archery Tag" arrows be correct?
There is a new sport called "Archery Tag" that involves shooting opponents with foam-tipped arrows fired out of a real bow. The official Archery Tag web site presents data that claims to show the ...
- 209
4
votes
1
answer
2k
views
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
4
votes
1
answer
186
views
Why is the kinetic energy a fixpoint of the Legendre transformation?
Question: Why is (from an intuitive standpoint) the kinetic energy $T$ a fixpoint of the Legendre transformation, i.e. $\frac{\partial T}{\partial \dot q}\dot q-T = T$ for any general coordinate $q$? ...
- 315
4
votes
0
answers
166
views
Why is the ratio of components of kinetic energy equal to the ratio of kinetic energy to total energy for a projectile whose range is maximized?
The launch angle $\theta$ that maximizes the range of a projectile in a uniform gravitational field is
\begin{align}
\theta = \arctan\left(\frac{v_o}{\sqrt{v_o^2 + 2gh}}\right), \tag{1}
\end{align}
...
- 41
3
votes
3
answers
893
views
Newton's Second Law in vertical launch of a rocket
Consider a rocket being launched vertically.
Let $T(t)$ denote the thrust from the engine and $M(t)$ be the total mass of the rocket at time $t$.
At $t=0$, $T(0)=M(0)g$ (so that the normal force due ...
- 1,047
3
votes
4
answers
249
views
Irreversibility Aristoteles law of motion
I am watching the second lecture from the theoretical minimum and do not understand the argumentation of Susskind.
For those who do not want to watch the video. It is about the law of motion from ...
- 573
3
votes
3
answers
881
views
Is there an intuitive explanation of the work formula?
Upon learning calculus, I decided it was time to derive all of classical mechanics to give myself a good understanding of physics. What I found was that, while trying to do so, I would need some ...
- 566
3
votes
1
answer
302
views
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
3
votes
2
answers
197
views
Physical meaning of $dx/dt$ for objects of changing length
I was solving '200 Puzzling Problems in Physics' as a recreational activity and I encountered this beautiful question which surprised me as I understood a basic flaw in my conceptual understanding.
...
3
votes
2
answers
254
views
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
3
votes
2
answers
4k
views
Elastic collision between two circles [duplicate]
I am trying to calculate the final velocities of two equal mass 2-dimensional circles after an elastic collision. I have tried to figure it out using formulas I know from high school physics, but ...
user99752
3
votes
3
answers
1k
views
A particle of mass $m$ moves with constant speed $v$ along the curve $y^{2}=4a(a-x)$ [closed]
I have complications to do the following problem:
A particle of mass $m$ moves with constant speed $v$ along the curve $y^{2}=4a(a-x)$. Find its velocity and acceleration vectors.
My first idea was ...
- 159
3
votes
1
answer
483
views
Kinematics on affine spaces
I was reading Arnold's Mathematical Methods in Classical Mechanics and it's not clear to me what exactly he's trying to achieve by introducing an affine space to model the set of all "positions in the ...
- 63
3
votes
2
answers
884
views
Why is energy not conserved in this situation
Suppose there are three masses that are still relative to each other in space. They are positioned in an equilateral triangle. Let's accelerate one mass towards the other two with a force. The energy ...
user86425
3
votes
1
answer
1k
views
finding velocity along a curve with kinematic equations using time
(i'm "not" looking for coding help. i need help setting up the math.)
i'm writing a program for a physics class to find the velocity of an object across a random curve. where the only force acting on ...
- 31
3
votes
3
answers
2k
views
Does material (density) affect falling rate of objects? [duplicate]
Suppose Galileo dropped a one-kilogram ball of cotton and one-kilogram ball of iron from the top of the Leaning Tower of Pisa, then which one will reach the ground first?
Assume that the cotton ball ...
- 423
3
votes
1
answer
137
views
Average Velocity ($\vec{\bar{v}}$) Intuition and Analogy for Non-Uniform Acceleration
Background
So I was trying to make as much sense out of kinematics through intuition after having taken my first semester of university physics, and I've stumbled onto a dillema that I can't seem to ...
- 66
3
votes
1
answer
241
views
In real life, why is space of states or state-space defined only by position and velocity?
My book defines state-space as "the collection of all possible states of the system." For example, the state-space of a coin is heads or tails. It also said that in our world, state-space is defined ...
- 128
3
votes
1
answer
746
views
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
5k
views
Hockey puck collision [closed]
I have a homework question in which a sticky hockey puck traveling at constant velocity parallel to the side of the rink strikes a stationary puck and sticks to it. The angels between centres at ...
- 316
3
votes
1
answer
242
views
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
3
votes
0
answers
62
views
Why does the photon in Compton Scattering have a minimum frequency/maximum wavelenght?
Using conservation of four-momentum one finds that, with respect to the angle of deviation of the photon from its original direction $\theta$, the wavelength and frequency of the emitted photon are:
$
...
- 423
3
votes
3
answers
444
views
Velocity after applying a force in the vacuum
I’m sorry for so simple question, but I just need to be sure.
I understand, that the changing of the speed occurs only when the force is applied, I understand that if one punch a ball in the free ...
- 143
3
votes
2
answers
127
views
How to decelerate from velocity $v$ to stop time $t$ over distance $d$? [closed]
I'd be grateful for some help with this problem I am trying to solve.
Let's say that I have an object travelling at a velocity $v$. I want that object to come to a halt in time $t$ AND travel exactly ...
- 31
3
votes
0
answers
419
views
Is there is an entropy cost of moving an object?
Is there an entropy cost associated with moving an object from one point to another, even if all forces involved are conservative? Or, is there some condition on what kind of move has an entropy cost?
...
- 33.4k
2
votes
3
answers
721
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I am moving right and rain is falling vertically down.Why should I hold umbrella at an angle?
This is related to relative velocity.I get that, from my moving frame of reference rain is making an angle.But still... it doesn't make sense to hold umbrella at an angle when rain is falling ...
2
votes
3
answers
246
views
Why does this example seem to contradict conservation of energy?
Consider a 10 kg box on the bed of a truck accelerating at 1 m/s^2. Consider a reference frame where it starts at 0 m/s and ends at 10 m/s and then consider a reference frame where it starts at -5 m/s ...
- 392
2
votes
2
answers
284
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Acceleration without a force in special relativity
Let us consider a relativistic particle of mass $m$ and charge $q$ in a constant electric field $\mathbf{E}=E\mathbf{\hat{j}}$ moving in two spatial dimensions, a relativistic extension of the well-...
- 1,112
2
votes
4
answers
356
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Acceleration and Circular Motion
Lets assume that there is a force that makes our body moves in circular motion.
We know that the acceleration of a body that moves in circular motion is Velocity ^ 2 / Radius .
How is it ...
- 407
2
votes
2
answers
224
views
Difference in answer using relative motion and that without (Newtonian Mechanics)
The question:
Two bodies move in a straight line towards each other at initial velocities $v_1$ and $v_2$ and with constant accelerations $a_1$ and $a_2$ directed against the corresponding ...
- 123
2
votes
2
answers
2k
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Why doesn't the optimal angle (for maximum range) on an inclined plane equal 45 degrees?
Observe this case
The goal is to maximize $d$ by increasing the angle of the initial velocity. Since we know that the range is maximum for $\theta=45^\circ$ I would reason that the jumping ramp has ...
- 332
2
votes
1
answer
971
views
Circular motion problem? [closed]
I am learning about circular motion and not quite sure how to approach this particular problem. Any help would be greatly appreciated!
A particle moves along a circular path over a horizontal $x$-$...
- 161
2
votes
3
answers
883
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Minimum velocity of projectile with air resistance not at top?
Suppose I have a projectile motion without friction, the minimum velocity is always at the top.
Now I read that with friction the minimum velocity is not always at the top? Is this true? If yes, why?
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