14 votes

Trying to understand Newton's Second Law

It is normal that an object has a constant velocity while we apply a constant force. But it is an indication that there is another force acting in the opposite direction, usually some friction force. ...
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9 votes
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How could any frame of reference be inertial?

In newtonian mechanics, inertial frames are an equivalence class. They can be defined as frames where Newton's laws are valid. If you can find one inertial frame, then you automatically get an ...
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  • 682
6 votes

Trying to understand Newton's Second Law

My thinking here is that change in position means change in velocity This is wrong. A change in position does not necessarily mean a change in velocity. If an object is moving at a constant velocity ...
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  • 7,113
6 votes

Trying to understand Newton's Second Law

$a$ is the rate of change of velocity. So if $a$ is zero, $v$ is constant and doesn't change over time. So while you're applying a force, the velocity is changing and $F=ma$. After the force stops, ...
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  • 397
6 votes
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Meaning of "$=$" in $\vec{F}=m\vec{a}$ (for example)

I don't understand how the two could really be one and the same. E.g. we can exert forces $F$ and $-F$ on a body and it's acceleration will not change. $\vec{F}$ in the $\vec{F}=m\vec{a}$ is the net ...
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4 votes

Helicopter hover flight question

For this kind of problem, I find it easier to think about momentum than about mass and acceleration. Remember that momentum is mass times velocity, $$ \vec p = m\vec v $$ and so Newton's second law ...
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  • 70.2k
3 votes

With how many Newtons of force is the universe expanding?

To give a more concrete scenario for my question: two neutrons are in free space. At what rate will they accelerate away from each other (due to the expansion of the universe)? Does it depend on the ...
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  • 2,824
3 votes

Why do kinematic equations only work with constant acceleration?

Why do kinematic equations only work with constant acceleration? In general, in one dimension: $$ \frac{dv}{dt} = a(t)\;, $$ where the acceleration $a(t)$ is a function of time. Integrating both ...
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  • 7,113
3 votes

Meaning of "$=$" in $\vec{F}=m\vec{a}$ (for example)

In physics equations (as in mathematics), symbol "=" (equals) means equality in value, not identity of concepts. So in the equation $$ \mathbf F = m\mathbf a $$ the two sides are not "...
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2 votes
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Maximum height reached by an object

Here, in the last line, from the formula s is negative, but how can s be negative? It's a typo. Also, should it not be s=u^2/2g instead of s= - u^2/2g? Yes.
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  • 7,113
2 votes

Does time beyond a Rindler horizon run backwards in the accelerating frame?

Is time inversion every bit as physically real as time dilation? … If your answer is that it's not as physically real (e.g., that it's the result of coordinate changes) Time inversion is every bit as ...
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  • 64.4k
2 votes

Why does velocity change or accelerate in the presence of force?

Well okay, this is a tricky one. First recall when is the equation $F=ma$ valid. You may know that it is valid in a special class of frames of reference, known as inertial frames. So now the question ...
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  • 73
2 votes

Layman question about relativistic motion

establish my measurements Let's say that in my reference frame I am at rest, and in the middle. I observe Alice moving toward me to the right at $\frac{3}{4} c$, and I observe Bob moving toward me to ...
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  • 5,370
2 votes

Length contraction and acceleration in opposite directions

When you accelerate right from rest to $0.9c$ you are quite correct that distances are Lorentz contracted so the distant objects get nearer to you. However if you now start accelerating left your ...
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2 votes

Why do kinematic equations only work with constant acceleration?

It's pretty simple. The formal definition of velocity is the derivative of position with respect to time. So in one dimension: $v = \frac{dx}{dt}$ And therefore $x(t) = \int_{0}^{t}v(t')dt'$ If you ...
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2 votes
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Why do kinematic equations only work with constant acceleration?

Kinematic equations, one of which is $v=u+at$, are derived making the assumption that the acceleration $a$ is a constant. Why this is so can be seen by inspecting a graph of velocity against time for ...
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  • 77.1k
1 vote

Trying to understand Newton's Second Law

There's two things to note here. The first one is that both quantities $\mathbf{F}$ and $\mathbf{a}$ are actually functions of time, not just numbers. If one wants to be explicit, one can write this ...
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1 vote

Trying to understand Newton's Second Law

If I apply a force on an object at rest and it’s velocity is constant This is not possible. Newton's first law already says that if you apply force, velocity will change. So the situation you ...
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  • 11
1 vote

Why do kinematic equations only work with constant acceleration?

The fundamental equations describing Newtonian mechanics are differential equations. Newton's Second Law (for the position $\vec{x}$ of single mass) takes the form $$m\frac{d^{2}\vec{x}}{dt^{2}}=\vec{...
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1 vote

Why does Newton's second law involve mass?

Newton's second law states that the force experienced by a body is vectorially equal to the rate of change of its momentum which is defined as mv. For a fixed mass, this rate reduces to the familiar ...
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1 vote

Meaning of "$=$" in $\vec{F}=m\vec{a}$ (for example)

To add on top of good answers already present: I don't think it makes sense to say that a body at rest is accelerating equally in all directions In a way it does. Acceleration is a vector quantity. ...
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  • 5,471
1 vote

Helicopter hover flight question

When analysing a fan, propeller or engine which isn't moving, the air which is being sucked through the rotor starts far away and not moving. Air is drawn in from all around, so the area far away is ...
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  • 397
1 vote

Time derivative of unit velocity vector?

As the magnitude of a unit vector cannot change, $\dfrac {d\hat v}{dt}$ is related to the rate of change of the direction of the velocity.
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1 vote

Distance contraction and acceleration

Your diagrams are incorrect. The distance between two points is frame dependent. In the frame in which the two points are stationary, the distance is known as the 'proper' distance between the points. ...
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1 vote

Ball attached to string snaps in decelerating car

The ball has forward momentum and will keep going with constant speed forward. At the same time, gravity will accelerate it downwards so it will start moving downwards as will. From the outside this ...
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  • 3,230
1 vote

Splitting gravity along $x$, $y$, and $z$ axes

I think what you are asking is if you have a vector $\vec{g}$ defined in terms of the world directions $\hat{i}$, $\hat{j}$ and $\hat{k}$, how do you express this vector in the body directions $\hat{u}...
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1 vote

With how many Newtons of force is the universe expanding?

Zero for both proper acceleration and force. There is no proper acceleration associated with expansion. See: wikipedia for the difference between proper acceleration, which corresponds to forces and ...
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  • 8,578
1 vote
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If I hang from the ceiling of the elevator which is falling freely then will I experience weightlessness?

Instead of feeling less force by the floor pushing up on your feet if standing on the floor, you will feel less force pulling up on your arms by the stick or rope or whatever it is you are hanging on. ...
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  • 55.6k
1 vote
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What would happen if when falling down you get pushed up?

It depends on how hard you can push. Realistically, it would not have much effect. After all, the height at which you can throw a person is negligible compared to $10$ meters. Btw, at such heights, ...
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  • 1,157
1 vote

Layman question about relativistic motion

The formula for adding two velocities $u$ and $v$ in the same direction is $$V= \frac{u+v}{1+uv/c^2}$$ For velocities much less than $c$, the everyday formula $V\approx u+v$ holds true. You can try ...
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