All Questions
Tagged with classical-mechanics kinematics
255 questions
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How should I think about a block-and-tackle configuration weight-lifting machine?
At my gym, some of the weight machines provide a double mechanical advantage using a gun tackle pulley configuration.
For a long time when I was using such machines, I convinced myself that if I were ...
- 339
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1
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1k
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Calculating an "apparent" speed of a beam in a medium
While thinking about relativity, one question sparked my curiosity. If we could observe the trajectory of a light beam by using some partially opaque medium, like smoke, to make it visible, we'd not ...
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101
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Move body in 1-dimension to desired state by applying force
Consider a simple point mass of $M$ in vacuum in 1-dimension with initial position $x_0$, velocity $v_0$ and acceleration $a_0$. Our goal is to move this body to position $x_1$ with velocity $v_1$ and ...
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241
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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 ...
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2
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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 ...
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Intuition - why does the period depend on the amplitude in a pendulum?
I'm looking for an intuition on the relationship between time period and amplitude (for a large pertubation) of pendulums. Why does the period depend on the amplitude? I know the math of the problem. ...
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897
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Intuition for the velocity ellipsoid
The velocity ellipsoid is a quantity that comes up in the kinematic modelling of N-body systems, e.g. stars in a galaxy. The velocity dispersion tensor describes the local distribution of velocities ...
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Acceleration in plane polar coordinates [duplicate]
When we express acceleration in plane polar coordinates, we can find that
$\vec{a}= \left(\ddot{r} - r \dot{\theta}^2\right)\hat{r} + \left(r \ddot{\theta}-2\dot{r}\dot{\theta}\right)\hat{\theta}$.
...
user174490
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Projectile motion question : time at which velocity v becomes perpendicular to initial velocity u? [closed]
A projectile is thrown up with the initial speed u, making an angle theta (theta > 45 deg) with the horizontal. What is the time, just after which, it will be moving perpendicular to its initial ...
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I have an idea which would produce a minuscule delta-v without expending mass. Would it work? Why or why not? [closed]
The idea is that an electromagnetic cannon shoots a rubber ball that contains a core of ferromagnetic matter into a box. The box closes and the ball will bounce back and forth with increasingly lower ...
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161
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How do we generalize from a scalar (one dimensional) equation is transformed into a vector (multidimensional) equation?
I was reading about Work-Energy theorem recently and they first derived it for a constant force. So, they wanted to use the equations of motion which they derived for one dimensional constant ...
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Computing angular acceleration of a composition of coordinate frame transformations
Given two coordinate frames $A$ and $B$, we can define the transformation between them by:
$[\vec r_{AB}]_A$, the vector from the origin of $A$ to the origin of $B$ (resolved in frame $A$), and
$q_{...
- 633
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3
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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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Kinematic Approach
I was recently looking at a physics problem and it kind of confused me:
A 1 kg ball is shot out of a 5m long cannon directly upwards. A constant force of 15 N is used to accelerate the ball out of ...
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419
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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?
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Kinetic energy is different in different frames of reference? [duplicate]
If velocity is a relative term then a body would possess different Kinetic Energy in different frames of reference.
How can a body have different energies simultaneously for different observers ?
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Change in center of rotation of an object
Please refer to the figure below. The center of mass of the rod under the net force will accelerate. At the same time, the whole rod will also rotate around its center of mass. In his lectures, ...
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How to show angle between velocity and acceleration vector is constant in polar co-ordinates? [closed]
In polar co-ordinates we have
$\vec{r} = r\hat{r}$ and
$\vec{v} = \dot{r}\hat{r} + r\dot{\theta}\hat{\theta}$ and
$\vec{a} = (\ddot{r}-r\dot{\theta}^2)\hat{r} + 2\dot{r}\dot{\theta}\hat{\theta}$
...
- 293
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1
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When one kid runs into another and they bump heads, why is the slowest mover in most pain? [closed]
In my experience, if one kid runs really fast and accidentally bumps into a second kid who's standing still, and they bump heads, the kid who was 'standing still' (relative to earth) always seems to ...
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483
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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 ...
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Time for bead to slide along the chord of a vertical circle
I ran into this problem in my mechanics homework.
Here's my go at it. I hit a wall at the end and I just don't know what to do.
assuming this circle
Please note that $\alpha \neq 90$ degrees. It's ...
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How long, and where, can you stay dry under an idealized tree when rain is falling, and there is no wind?
Imagine, when no wind is blowing, rain is falling on an ideal tree: It has a one-dimensional vertical rigid trunk with one-dimensional single rigid branches perpendicular to the trunk (see picture 1, ...
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2
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Calculating the acceleration that can be done before stopping is impossible in a given distance
My basic problem is this:
In a frictionless environment, I have an object traveling at a known speed that has a known maximum deceleration rate and a known distance to move before it must stop. I ...
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250
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Deriving an expression for the tangential velocity of a meteor orbiting the Earth? I have 2 expressions, not sure which is correct [closed]
"A meteoroid of mass $m$ is on a circular Earth orbit of radius $R$ which is a few (> 2) times larger than the radius of the Earth $R_E$. Derive an expression for the meteoroid's speed. State the ...
- 1,327
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81
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Determine if Reynolds Number is large or small in classical mechanics. [duplicate]
In classical Mechanics, there is a reference to the Reynolds Number ( Re=ρvd/η (ρ density, v velocity, d diameter and η the viscosity of fluid)) that relates the ratio $$ f_{\text{quadratic}}/ f_{\...
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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, ...
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3
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521
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What is really instantaneous?
How can a body travel at an instant and what does instantaneous speed tells us?
What really is meant by speed of an object at an instant if an object does not travel at an instant? I would like a ...
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Why shall we study mechanics after newtons laws of motion
I have heard and read that the 3 laws of motion are sufficient to solve any problem in classical mechanics, if its true then why we study concepts like work energy, conservation of momentum, centre of ...
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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 ...
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254
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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 ...
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Collision of bullets with dish to hold it in space.
A dish of mass $10\ g$ is kept floating horizontally in the air by firing bullets, each of mass $5\ g$, with the same velocity, at the rate of $10$ bullets per second and the bullets rebound with the ...
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4
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Uniform Circular Motion w/ Tension and Friction
So I had a problem today which I couldn't make any sense of. I don't have access to it at the moment but this is a pretty accurate approximation.
Basically, a mass (m) is swinging horizontally on ...
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576
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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 (...
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Difference between "Periodic motion" and "Oscillating Motion"
So far I know one of them is a special case of the other: The Oscillating motion being the special case of Periodic motion. But I don't know the precise "Kinematical definition" of each one. I mean ...
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884
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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
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1
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Calculating velocity of a car based on engine power
Is it possible to calculate the velocity of a car accelerating from rest at full capacity given the power of the engine and the mass of the car? I have a method of solving the velocity with respect to ...
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What does it mean to find an equation of motion, given vector functions that describe both the object's position and velocity?
I don't really understand how to approach a problem that asks to find the equation of motion. Intuitively, I would guess that an "equation of motion" is an equation where the particle's position is ...
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2
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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 ...
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4k
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Two objects moving in the same direction; when do they meet? [closed]
I'm awful at physics and need help with a homework problem from my textbook. It reads as follows:
You are standing at rest at a bus stop. A bus moving at a constant speed of $5.00 \;\mathrm{m/s}$ ...
user129677
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Why is my proof for centripetal acceleration given uniform motion wrong?
I was trying to make my own proof for centripetal acceleration (a = (v^2)/r).
I took two points along the path of motion A and B, which are a distance (along the circle) of half the circumference of ...
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2
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Intuition behind the $\frac{1}{2}$-fraction in $s(t) = \frac{1}{2}v(t)t$ for motions with constant acceleration
I'm refreshing my mechanics knowledge and have a question.
Say we have an object moving with a constant acceleration $a$ moving in one dimension. Furthermore, $v_0 =0$, $s_0 = 0$ and $t_0 = 0$ (with $...
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Projectile question doubt [closed]
A hunter wants to shoot a monkey with an arrow by launching the arrow at a speed $v_0$ at a distance of $L$ from the base of a tree of height $H$ on which the monkey is sitting. Now on watching the ...
user118752
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2
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2k
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Average acceleration: why I am getting different results?
Let's consider a simple school problem.
A car starts moving during 3 seconds with a constant acceleration of 1 m/s^2.
Then it stops accelerating and moves 3 seconds more with a constant speed.
Find ...
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1k
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non constant acceleration problem [closed]
The acceleration of an arrow from a bow falls from $6000m/s^2$ to zero when it leaves the bow after travelling a distance $x=0.75m$. Assuming that this acceleration can be expressed by the linear ...
2
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2
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1k
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Does the position-time graph have to be a smooth function?
If at some time $t$ there were a discontinuity in the velocity-time graph, then the acceleration would be infinite at $t$. So intuitively, it seems that the velocity-time graph must be continuous. I ...
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Impulse Equations
A solid sphere of mass $m$ rolls without slipping on a horizontal surface and collides with a vertical wall, elastically. The coefficient of friction between the sphere and wall is $\mu$. After the ...
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4k
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Motion of an object in a moving car and collison
I came across an interesting question today at work.
'Imagine traveling in a car. The passenger has a glass bottle in their hand. In which direction relative to the moving car should the passenger ...
user105149
3
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1
answer
1k
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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 ...
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2
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4k
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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
0
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2
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119
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A drop falling in the condensed air
A drop is falling in humid air with air resistance equal $F_r = - \alpha v^2$. In $t = 0$ the drop is ideally spherical, $h$ above the ground, has mass $m_0$ and velocity $v_0 = 0$.
What mass and ...
