All Questions
45 questions
13
votes
7
answers
3k
views
Can we divide a vector by another vector? How about this: $a = vdv/dx?$
My physics teacher told us that we can’t divide vectors, that vector division has no physical meaning or significance. How about this: $$a = vdv/dx.$$
It says acceleration vector equals velocity (as ...
- 876
6
votes
2
answers
1k
views
Terminology for time derivative of speed (not velocity)
Is there any standard terminology for the derivative of the magnitude of velocity with respect to time (suitable for use in first-year Calculus)? The word ‘acceleration’, in its technical sense, is ...
- 201
4
votes
2
answers
261
views
The acceleration of circulation motion
We know that in circular motion the position vector is $r\hat{r}$. Then the velocity is the time derivative of it. So it gives $$dv/dt = r d\hat{r}/dt + \frac{dr}{dt} .\hat{r}.$$ now I can't ...
- 1,159
4
votes
2
answers
861
views
Integration of tangential acceleration with respect to time
Here, by tangential acceleration, I mean the component of acceleration along the velocity vector.
What do you get when you integrate tangential acceleration with respect to time? What does the '$v$' ...
- 1,106
3
votes
1
answer
133
views
Contradiction of a scalar product
Can anyone resolve this contradiction:
$$\vec{r}\cdot\dot{\vec{r}}=\frac{1}{2}\frac{d}{dt}\left(\vec{r}^2\right)=\frac{1}{2}\frac{d}{dt}\left(\left|\vec{r}\right|^2\right)\equiv\frac{1}{2}\frac{d}{dt}...
- 393
2
votes
3
answers
193
views
Is $ d \mathbf v · d \mathbf v = d \mathit v^2 $?
My teacher has proved the following:
$$ \mathit v^2 = \mathbf v·\mathbf v = \frac{d\mathbf r}{dt}·\frac{d\mathbf r}{dt} = \left(\frac {ds}{dt}\right)^2 \Rightarrow \mathit v = \frac{ds}{dt} $$
Because ...
- 23
2
votes
4
answers
20k
views
How to find tangential/radial/angular velocity for motion in any curve? [closed]
Is the radial velocity responsible only for changing distance between objects and the component perpendicular to it only for change in direction? If so why?
Please try to give a different explanation ...
- 188
2
votes
1
answer
292
views
Is the relation "slope=velocity" mathematically valid?
$\text{Slope= tan(angle with respect to positive X-axis)= scalar output}$
$\text{velocity= a vector }$
Source: Hugh D Young_ Roger A Freedman - University Physics with Modern Physics In SI Units (...
- 439
2
votes
3
answers
179
views
Difference between $|d{\bf r}|$ and $d|{\bf r}|$
What is the difference between $|d{\bf r}|$ and $d|{\bf r}|$ and why are both of them not always equal to each other?
My question might seem stupid to some and will probably get downvoted but I have ...
- 733
2
votes
1
answer
125
views
Vector Derivative: General Case
From "An Introduction to Mechanics" by Kleppner & Kolenkow, SIE-2007, Chapter 1 (Vectors and Kinematics), Section 1.8 - "More about the derivative of a vector".
In this section, towards the end, ...
- 203
1
vote
1
answer
94
views
Simple difference between module of velocity and time derivative of module of position [duplicate]
What is the conceptually difference between the two:
$$\frac{d|\vec{r}|}{dt}=\frac{\vec{r}\cdot\frac{d\vec{r}}{dt}}{|\vec{r}|}\neq|\dot{\vec{r}}|\equiv \bigg|\frac{d\vec{r}}{dt}\bigg|$$ ...
- 189
1
vote
5
answers
7k
views
Direction of velocity vector in 3D space
According to a well-known textbook (Halliday & Resnick), the direction of a velocity vector, $\vec v$, at any instant is the direction of the tangent to a particle's path at that instant, as is ...
- 113
1
vote
3
answers
233
views
Problem with the constant magnitude of vectors if the change in the same vector is perpendicular to it [duplicate]
Note: I am merely a highschool student attempting to self-study Classical Mechanics, some of the assumptions I make are perhaps wrong, so please bear with me. Thank you.
This while can be condensed ...
1
vote
2
answers
159
views
One object moves along the cycloid at a constant rate, how about its acceleration? [closed]
We know that the parametric equation:
$$x=R(\theta+\sin(\theta))$$
$$y=-R(1+\cos(\theta))$$
and the constant velocity $c$.
How do I prove that the acceleration of the object in the $y$ direction is ...
- 21
1
vote
1
answer
130
views
On the derivative of a vector function
In "An Introduction to Mechanics" by Kleppner and Kolenkow, in the section on the time derivative of a vector:
Given $A(t)$ is a vector valued function, then,
$$\Delta A = A(t + \Delta t) - A(t)$$
...
- 179
1
vote
1
answer
554
views
Meaning of normal acceleration?
acceleration means the rate of change in velocity (vector quantity) and the differentiation means to divide a certain quantity into small elements (i.e $dx$) as we do to find the acceleration at any ...
- 33
1
vote
0
answers
74
views
Does the proper four-acceleration $A^{\mu} = (0,0)?$
Let the proper four-position vector $x^{\mu}(\tau) = (0, \tau)$. Differentiating this successively wrt $\tau$ I get the four-velocity $u^{\mu}(\tau) = (0, 1)$ and then the four-acceleration $A^{\mu}(\...
- 3,148
1
vote
6
answers
113
views
If a body moves along a path (any path, not just circular) with constant speed, is it's tangential acceleration necessarily zero?
If a body moves along a path (any path, not just circular) with constant speed, is it's tangential acceleration necessarily zero?
I could only find general proofs for the case of circular motion and ...
0
votes
2
answers
353
views
Why isn't tangential acceleration just always 0?
This is probably a very stupid question but I can't help me.
Tangential acceleration is $\vec{a_t}=\frac{dv}{dt}\frac{\vec{v}}{v}=\frac{\vec{v} \cdot \vec{a}}{v} \frac{\vec{v}}{v}$. Since $\vec{a}$ is ...
- 15
0
votes
3
answers
84
views
How is velocity defined in circular motion in central force field?
In my view the velocity is change of displacement in the increasing direction of displacement. Now in circular motion in central force field the particle is changing its direction then how is the ...
- 1,159
0
votes
2
answers
5k
views
How is the direction of the instantaneous acceleration determined?
I know from the text book that the direction of velocity at any point on the 2D path of an object is tangential to the path at that point and is in the direction of motion. But how would one determine ...
- 941
0
votes
1
answer
78
views
Why do we neglect $\Delta t^2(\frac{d\vec{r}}{dt}\frac{d\vec{\hat{r}}}{dt})$ at Taylor Expansion?
I'm just started to Ankara University Physics Department two weeks ago. I have missed my 2 hours of PHY105 course that is the last week Wednesdey. The subject that i missed was Derivatives of Vectors. ...
- 709
0
votes
1
answer
248
views
Non-uniform circular motion with constant radius of curvature [closed]
$\let\oldhat\hat
\renewcommand{\vec}[1]{\mathbf{#1}}
\renewcommand{\hat}[1]{\oldhat{\mathbf{#1}}}$
Suppose we have a car moving on a circular track of radius $b$ and speed $v=ct$, where $t$ is time ...
0
votes
1
answer
156
views
Which relation is correct for resultant instantaneous velocity in 2d?
Please forgive me if the following question sounds silly and I can't exactly pin point where exactly the problem is but there is some problem with my understanding of vectors.
In Cartesian ...
- 93
0
votes
1
answer
90
views
Derivative of the product of a scalar function and a vector valued function
According to Berkeley Physics Course, Volume 1 Mechanics,
The time derivative of a vector valued function can be derived from the formula:
$$
\mathbf{r}(t) = r(t)\mathbf{\hat{r}}(t)
$$
where the ...
- 25
0
votes
2
answers
414
views
Why does tangential acceleration become 0 when the velocity is max? [closed]
I know that tangential acceleration equal to zero when the circular motion is uniform, but why is it equal to zero, when the velocity is max or min? Because there is no relation between the value of ...
- 11
0
votes
2
answers
180
views
Why is the magnitude of velocity negative in this example?
Magnitudes are positive values, but when I take, for example: the magnitude of a position vector: $r = 3 - 0.04t^2$ and try to take the derivate of it, the result will be $v = -2 * 0.04t$ which is a ...
- 165
0
votes
1
answer
129
views
Why intuitively is the tangent vector the derivative of velocity of position with respect to their modulus?
When trying to find the tangential velocity, many textbooks define the tangent direction as one of the following:
or
Intuitively, why is the tangent vector the derivative of the position with ...
- 849
0
votes
1
answer
225
views
The time derivative of a vector not defined in terms of the time variable $t$
Recently I got a question where I needed to determine the time derivative of a position vector. However, the vector didn’t have the variable $t$ but instead had $x$, $y$, and $z$ as its terms, so I ...
- 193
0
votes
3
answers
1k
views
How to determine the direction of instantaneous acceleration in a 2D motion? [duplicate]
How do we determine the direction of instantaneous acceleration when the body is moving in a plane (or a 3D space)? This question has been truly bothering me for nearly two weeks. I looked it up, ...
- 876
0
votes
1
answer
100
views
Why trajectories approach to origin tangent to the slower direction?
I am reading non-linear dynamics from Strogartz. Suppose, I have two solutions of a non linear system: $x(t) = x_0e^{at}$ and $y(t) = y_0e^{-t}$, where $a\in \mathbb{R}$. Now it is clear that,for $a&...
- 27
0
votes
1
answer
43
views
Are terms tangential acceleration and normal acceleration only used for instantaneous velocity?
Are terms tangential acceleration and normal acceleration only used
for instantaneous velocity?
- 23
0
votes
0
answers
55
views
What do you call $ \frac{d^2 r}{dt^2}$ in polar coordinates? [duplicate]
In polar coordinates, one finds centripetal acceleration as:
$$ a_c = \frac{d^2 r}{dt^2}- \frac{v^2}{r}$$
Where $|r|$ is distance from center to particle, $v$ is tangential velocity.
My question is ...
- 8,040
0
votes
0
answers
46
views
1/velocity for higher dimensions
I have a somewhat basic question. I am sorry if it trivial.
Denote the velocity by $v=\frac{dx}{dt}$ suppose that $x \in \mathbb{R}^n$ and I want to parametrize $t$ in $x$ and compute $\frac{dt}{dx}$. ...
- 103
0
votes
0
answers
152
views
Product rule for 4-vectors and derivation of 4-force form
In deriving the form for the 4-force in special relativity, we begin with
$$\frac{d}{d\tau}p^{\alpha}=m\frac{d}{d\tau}u^{\alpha}=f^\alpha$$
where $\tau$ is the proper time, m is rest mass.
Since $...
0
votes
1
answer
87
views
What mean this momentum-derivative?
I'm working with quantum gravity. I have to make a Taylor-series. I got some help for this, but I have problem with understanding the formalism. So, I have the operator $A((P-p)^2)$, which needs to ...
- 3
0
votes
2
answers
84
views
Acceleration in a non-inertial reference frome - derevation
The general velocity equation for a point B in on body rotating and translating about point A with respect to the inertial reference frame say 'xyzo' can be expressed as,
$\vec{r_{B/o}} = \vec{r_{A/o}...
- 17
-1
votes
2
answers
158
views
What does it mean for velocity to be a derivative of position, if position a point, not a function? [closed]
So in mass-spring simulation I encountered that one simulates particles by using positions and velocities of particles etc.
People may say that velocity is the derivative of position.
But isn't "...
- 459
-1
votes
2
answers
80
views
Problem with resources, Walter Lewin's third lecture
I've watched Walter's third lecture in 8.01 and I have a small problem with the last part, where he says that $$\vec r_t=x_t\cdot \hat x\ +\ y_t\cdot \hat y\ +\ z_t\cdot \hat z \\ \vec v_t=\frac{d\vec ...
-1
votes
2
answers
273
views
How can I show that the acceleration vector for uniform circular motion undergoes uniform rotation?
Does it suffice to show that the dot product between the acceleration vector and the derivative of the acceleration vector = 0?
- 39
-2
votes
1
answer
59
views
Need help in understanding Tangential Acceleration [closed]
I am studying Circular motion and I am confused about tangential acceleration and tangential velocity. I am studying uniform circular motion and it says the tangential acceleration is $0$ in uniform ...
-2
votes
3
answers
96
views
Why is it wrong to find centripetal acceleration using change of velocity over change of time?
This question asks to find the centripetal acceleration by giving the initial and final velocity over the change of time.
As shown, my book combined two rules to find the acceleration. I utterly ...
- 377
-2
votes
1
answer
91
views
From where does the expression of the tangential accerelation come from?
I've seen so many times that the expression of the tangential acceleration is known to be: $$a_t=\ddot{s}$$ but from the expression of the acceleration in spherical coordinates, in the tangential ...
- 69
-2
votes
1
answer
49
views
What does the derivative of tangent means? [closed]
While studying the circular motion I had to find the derivative of a tangent so I thought what the derivative of a tangent could probably mean since the derivative of position gives velocity.
Or think ...
- 1
-4
votes
1
answer
71
views
Given that $m \dot v \cdot v = 0$ , how is it equal to $m \frac{d}{dt} (v \cdot v)/2$? [closed]
While studying about scalar triple product in vector algebra, I stumbled upon the following question with the solution.
I want know how is $m \dot v \cdot v $ = $m \frac{d}{dt} (v \cdot v)/2$?
- 1