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Questions tagged [kinematics]

The description of the movement of bodies by their position, velocity, acceleration (and possibly higher time derivatives, such as, jerk) without concern for the underlying dynamics/forces/causes.

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223
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16answers
57k views

Why does kinetic energy increase quadratically, not linearly, with speed?

As Wikipedia says: [...] the kinetic energy of a non-rotating object of mass $m$ traveling at a speed $v$ is $\frac{1}{2}mv^2$. Why does this not increase linearly with speed? Why does it take so ...
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5answers
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Why are objects at rest in motion through spacetime at the speed of light?

I read that an object at rest has such a stupendous amount of energy, $E=mc^2$ because it's effectively in motion through space-time at the speed of light and it's traveling through the time dimension ...
26
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13answers
64k views

Recommendations for good Newtonian mechanics and kinematics books

What are some good books for learning the concepts of Kinematics, Newton laws, 2D Motion of Object etc.?
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16answers
172k views

How can momentum but not energy be conserved in an inelastic collision?

In inelastic collisions, kinetic energy changes, so the velocities of the objects also change. So how is momentum conserved in inelastic collisions?
16
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5answers
101k views

How to get distance when acceleration is not constant?

I have a background in calculus but don't really know anything about physics. Forgive me if this is a really basic question. The equation for distance of an accelerating object with constant ...
3
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3answers
3k views

Why does the amount of energy transferred depend on distance rather than time? [duplicate]

The change in energy of an object can be determined by the work equation, where work is the change in energy: $$ W = F \cdot d $$ I conceptualize the transfer of energy as simply a series of small "...
17
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3answers
1k views

Why there is a $\frac{1}{2}$ in the distance formula $d=\frac{1}{2}at^2$?

I'm preparing for my exam, but I have difficulties in perceiving why there is a $\frac{1}{2}$ in the distance formula $d=\frac{1}{2}at^2$?
8
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5answers
15k views

Speed of a fly inside a car

A couple of weeks ago I was travelling in a car (120 km/h approximately) and I saw a fly flying in front of me (inside the car, near my nose, windows closed). I wonder how was that possible. Does it ...
11
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3answers
53k views

How can an object's instantaneous speed be zero and it's instantaneous acceleration be nonzero?

I'm studying for my upcoming physics course and ran across this concept - I'd love an explanation.
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2answers
2k 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 ...
28
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7answers
127k views

Is two cars colliding at 50mph the same as one car colliding into a wall at 100 mph?

I was watching a youtube video the other day where an economist said that he challenged his physics professor on this question back when he was in school. His professor said each scenario is the same, ...
13
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5answers
1k views

Infinite series of derivatives of position when starting from rest

Suppose you have an object with zero for the value of all the derivatives of position. In order to get the object moving you would need to increase the value of the velocity from zero to some finite ...
7
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2answers
2k views

Physics of simple collisions

I'm building a physics simulator for a graphics course, and so far I have it implementing gravitational and Coulomb forces. I want to add collisions next, but I'm not exactly sure how to go about ...
2
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3answers
27k views

How to prove that a motion is Simple Harmonic Motion (SHM)?

I would like to know how one could show and prove that a given motion is simple harmonic motion. Once given an answer, I'll apply that technique to an example I am trying to figure out. Thank you ...
70
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14answers
138k views

What is the difference between “kinematics” and “dynamics”?

I have noticed that authors in the literature sometimes divide characteristics of some phenomenon into "kinematics" and "dynamics". I first encountered this in Jackson's E&M book, where, in ...
7
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6answers
2k views

Physical intuition for higher order derivatives

Could somebody give me an intuitive physical interpretation of higher order derivatives (from 2 and so on), that is not related to position - velocity - acceleration - jerk - etc?
2
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2answers
726 views

Why is $R\cos{a} = mg$ in circular motion compared and not $R = mg\cos{a}$?

Normally, if an object of mass $m$ is inclined to the horizontal at an angle $b$, we set the reaction force of the object on the inclined plane as $R = mg\cos{b}$ (if we resolve the force of gravity ...
0
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2answers
1k views

Tangential acceleration in circular motion?

A lot of my problems have objects moving in circular paths with tangential and normal components of acceleration. If the tangential component is non-zero though, the speed is changing so the radius ...
8
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4answers
5k views

Integrating radial free fall in Newtonian gravity [duplicate]

I thought this would be a simple question, but I'm having trouble figuring it out. Not a homework assignment btw. I am a physics student and am just genuinely interested in physics problems involving ...
2
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2answers
2k views

Motion of a rod struck at one end

Imagine a strong metal rod of uniform density and thickness floating in a weightless environment. Imagine it lies on an X-Y plane, with one end (A) lying at 0,0, and the other end (B) at 0,1. Then it ...
13
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3answers
8k views

Is it possible to have a rate of change of acceleration?

I know this may seem a weird question, but it always bothers me. My physics book (Resnick,Halliday,Walker), and also various sites never say anything beyond acceleration. But when a moving body is ...
9
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5answers
3k views

Should you run when under rain?

When it's raining, would you get less wet if you run or more wet? I think you will get less wet, because rain is coming down in a constant volume and if you run you will have a shorter amount of time ...
2
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2answers
1k views

How do I adjust the kinematic equations to avoid reaching speeds faster than light?

I like some 'science' in my 'science fiction', so I started crunching out the kinematic equations for some of the scenarios my characters are getting involved in, and ran smack dab into an issue. (...
2
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1answer
1k views

Are velocity and acceleration smooth quantities?

My thinking: acceleration corresponds to a force which is instantaneous, so the acceleration of a rigid body can be rather spiky (non-smooth) velocity (angular velocity) describes the ratio of ...
16
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3answers
3k views

How does anything move? [duplicate]

So in order for two things $A$ and $B$ to move apart, for example, relative to each other, $B$ can be set into motion away from $A$. This means that we have to increase $B$'s velocity and therefore ...
5
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4answers
2k views

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 ...
2
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3answers
7k views

Uniform Circular Motion

Why does the object not go inward, into the circle if the acceleration is inward? I think its because the velocity to outward? So they sort of cancel each other out? But if the speed is kept constant ...
3
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2answers
922 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 ...
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6answers
3k views

Why is speed defined like it is?

I have a rather basic, maybe even dumb, question. I was wondering why speed is defined as it is: $s = d/t$ Of course, what the equation means is not too difficult to understand. However, there are ...
22
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7answers
19k views

How can kinetic energy be proportional to the square of velocity, when velocity is relative?

Let's start with kinetic energy (from los Wikipedias) The kinetic energy of an object is the energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a ...
8
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2answers
5k 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 ...
6
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2answers
21k views

Why is average velocity the midpoint of initial and final velocity under constant acceleration?

Since average velocity is defined as$^1$ $$\vec{\mathbf v}_\mathrm{av}=\frac{\vec{\mathbf x}-\vec{\mathbf x}_0}{t-t_0},$$ where $\vec{\mathbf x}$ denotes position, why is this quantity equal to $$\...
12
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4answers
6k views

Static Friction - Only thing that can accelerate a train?

I'm a computer programmer that never studied physics in school and now it's coming back to bite me a bit in some of the stuff I'm being asked to program. I'm trying to self study some physics and I'...
8
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2answers
8k views

Why does a balloon spiral in the air instead of moving in a straight line?

When an air-filled balloon is released without its opening tied up, it moves in a circular path rather than a straight line. Why is that?
4
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3answers
2k views

What is the position as a function of time for a mass falling down a cycloid curve?

In the brachistochrone problem and in the tautochrone problem it is easy to see that a cycloid is the curve that satisfies both problems. If we consider $x$ the horizontal axis and $y$ the vertical ...
8
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4answers
2k views

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. ...
2
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8answers
2k views

Why is there a universal speed limit?

I am looking for an answer that does not rely on Special or General Relativity -and without recourse to the fact that the speed of light is frame invariant. Is there another way of showing this ...
17
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5answers
554 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., $...
16
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4answers
94k views

Why does a ball bounce lower?

If a ball hits the floor after an acceleration then why does it bounces lower? I mean the Energy is passed to the floor then why does the floor give back less Energy?
15
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2answers
51k views

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 ...
6
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2answers
2k views

Does a tire need to slip to generate force?

Recently, I have been doing some research on racing and tire modelling. While I was doing this, I encountered many curves like those shown below. (source: insideracingtechnology.com) While I ...
13
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4answers
3k views

How is Chasles' Theorem, that any rigid displacement can be produced by translating along a line and then rotating about the same line, true?

Chasles' Theorem in its strong form says: The most general rigid body displacement can be produced by a translation along a line (called its screw axis) followed (or preceded) by a rotation about ...
7
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3answers
2k views

Zeno’s Paradox of the Arrow

Premises And the Conclusion of the Paradox: (1) When the arrow is in a place just its own size, it’s at rest. (2) At every moment of its flight, the arrow is in a place just its own size. (3) ...
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1answer
328 views

Is it possible to rotate an angle on perfectly smooth ice?

You must start and end with the same pose. Prove it if you think you can't.
3
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4answers
508 views

if a body is stopped by means other than friction, where does energy go?

Suppose we have an object in space. say gravity is negligible, and the thing has a rocket on both sides. the thing fires one rocket for, say, 5 seconds. now it's moving. The object has kinetic energy. ...
2
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2answers
6k views

Is squared motor gearbox ratio proportional to inertia ratio?

I read an interesting article http://m.machinedesign.com/news/motor-sizing-made-easy It is very interesting, but I can not follow the 2nd last paragraph. I don't understand why it is true. ...
4
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2answers
116 views

Do integrals of position make any sense? Do they have an application? [closed]

I know that taking the derivative of position with respect to time defines what we call velocity, but I've never heard of physicist going in the opposite direction with position. Is there any ...
4
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3answers
458 views

When can one write $a=v \cdot dv/dx$?

Referring to unidimensional motion, it is obvious that it doesn't always make sense to write the speed as a function of position. Seems to me that this is a necessary condition to derive formulas like:...
1
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2answers
7k views

What will be the relative speed of the fly? [duplicate]

It has happened many times and i have ignored it everytime. Yesterday it happened again . I was travelling in a train and saw a fly (insect) flying near my seat. Train was running at a speed of ...
0
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1answer
220 views

Resolving vectors along axes

While solving problems involving constrained motion, such as that which the following picture describes, I am always confused about one aspect of the situation in question: In the above problem, it ...