All Questions
17 questions
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How do force and mass work with all derivatives of position?
I think if $F(t) = kt^0$ then $$x(t) = x_0 + v_0t + \frac{k}{m}\frac{t^2}{2!},$$ and if $F(t) = kt^1$ then $$x(t) = x_0 + v_0t + \frac{k}{m} \frac{t^2}{2!} + \frac{k}{m} \frac{t^3}{3!},$$ and so on, ...
- 31
3
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1
answer
79
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What do we get on differentiating the instantaneous displacement function?
I was doing kinematics when a silly question came to my mind. It is as follows:
When we differentiate $x(t)$ (position as a function of time), we get $v(t)$ (instantaneous velocity). Doing the reverse,...
- 137
1
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6
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113
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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 ...
4
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3
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2k
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What does "Just before" and "Just after" really mean in physics problems?
So I'm stuck in a dynamics problem that asks what is the acceleration of a body just after A, where A is the point that separates the motion of the body from a curvilinear path to projectile motion. ...
3
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3
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653
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Confusion about successive derivatives of position in circular motion
Suppose we define a unit vector $\vec r$ along radial direction for a particle in uniform circular motion at an angular frequency $\omega$. Then we can write:
$$\vec r = \cos(\omega t)\hat i + \sin(\...
- 326
2
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5
answers
346
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Significance of $\frac{dv}{dx}=0$
Suppose an object is moving with varying acceleration in time.
What does it mean when it hits a point where $\frac{dv}{dx}=0$?
Does it mean the object has hit maximum velocity?
Assume the object ...
- 77
4
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2
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312
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Force and Accleration
It's just a basic question I had when I was studying physics years back,
So acceleration have two equations
$$a=\frac{F}{m}$$
and
$$a=\frac{\text{d}v}{\text{d}t}$$
So by the first equation, if I'm ...
- 171
1
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4
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58
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Can we calculate centripetal acceleration by using this method $\frac{\mathbf v_2-\mathbf v_1}{T}$?
If we know the angle between two velocity vectors $\mathbf v_1$ and $\mathbf v_2$, and if we know the time $T$ it takes for the velocity to change from $\mathbf v_1$ to $\mathbf v_2$,then is it ...
- 315
0
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2
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299
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Velocity as a property
Is velocity considered to be a property like mass and weight that can be measured at a single moment in time, such as mass of X measured at time T1, or is it a property that needs to be measured over ...
0
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1
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303
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Computing total derivative of Kinetic Energy w.r.t time
I am confused as to how to take the total derivative $\frac{dKE}{dt}$, where $KE$ is the kinetic energy.
I know that $KE = 1/2 *m * \dot{\vec r} \cdot \dot{\vec r}$. From here, if I take derivative ...
- 111
0
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1
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112
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Where is the frame information in a time derivative of a physical vector in a moving frame using limits?
In the equation:
$$\left(\!\frac{d \vec r}{dt}\!\right)_{\!1}=
\left(\!\frac{d\vec r}{dt}\!\right)_{\!0} + \vec\omega_{01}\wedge\vec r$$
How could this be translated to a mathematical definition of ...
- 1
0
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3
answers
84
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How is velocity defined in circular motion in central force field?
In my view the velocity is change of displacement in the increasing direction of displacement. Now in circular motion in central force field the particle is changing its direction then how is the ...
- 1,159
-1
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1
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106
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Radius as a constant while deriving of formula for acceleration in circular motion [closed]
While deriving acceleration in circular motion, we differentiate $\vec{v}=\vec{\omega}\times\vec{r}$
Here we differentiate by product rule and write $\frac{dr}{dt}$ as $v$.
So we know $\vec{s} =\vec{\...
1
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1
answer
130
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On the derivative of a vector function
In "An Introduction to Mechanics" by Kleppner and Kolenkow, in the section on the time derivative of a vector:
Given $A(t)$ is a vector valued function, then,
$$\Delta A = A(t + \Delta t) - A(t)$$
...
- 179
-1
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1
answer
3k
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How to find Net Force with constant velocity? [closed]
Does having a constant velocity always make the acceleration equal zero?
For example: A 5 kg ball is moving at constant velocity of 15 m/s. What is the net force on the ball?
If the formula is $F_{...
0
votes
1
answer
2k
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Derivation of centripetal acceleration
While reading HC Verma chapter 7 circular motion I came across a derivation which I couldnt understand. I have marked my doubt with red. I don't understand from where +dw/dt [- i sine +j cos0] came ...
- 997
1
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2
answers
4k
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Free falling and bouncing back
My confusion arises with free falling body.
For a free falling body the displacement ~ time graph has a kink (at the time when the body hit the ground ). at a kink point, a function is not derivable ...
- 13