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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Forces at the interface between two blocks [closed]
Two blocks of masses m, and ma in contact lie on a horizontal smooth surface as shown in figure. The blocks are pushed by a force F. If the two blocks are always in contact, what is the force at the ...
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Angular velocity basics [closed]
Is angular velocity only defined for circular motion or can it be described for lets say projectile motion as well? (The particle is in projectile motion. Find it's angular velocity about point of ...
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Literature request - Dual quaternion dynamics
In my engineering practice, quaternions turned out to be much more practical than trigonometric rotation matrixes. I learned from this book on quaternions and dynamics how to describe rotation and ...
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Can we derive instantaneous horizontal velocity by getting instantaneous tangential velocity? [closed]
I have been stuck on this problem:
I have been able to all of them except Problem 38. I think we are expected to solve this with just kinematics and dynamics.
The approach I used is different than ...
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How to find acceleration of an object after being hit by another object and how long the acceleration last [closed]
By using conservation of momentum principle, we can calculate the velocity of an object after being hit by another object.
This can be done by assuming the velocity of the object that hits the other ...
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How to calculate the force needed to make the shopping cart move? [closed]
So I have this project, where I make a shopping-cart-gokart and I would like to calculate how much force is needed for the shopping cart to start moving.
The biggest issue I had is that I could only ...
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Projectile hits the top of sphere [closed]
I'm stuck on a particular projectile case in two dimensional motion. The case is when a projectile is thrown from some distance away from a sphere from the same horizontal plane on which the sphere ...
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How to Calculate the Stopping Distance of Train on a Complex Track [closed]
I am attempting to determine when a train should begin braking to reach a certain point at a complete stop. There are several factors that need to be considered that make this more complicated and I ...
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A man standing in an elevator at the third floor of a building. What is the primary factor that determines the man's kinetic energy?
Misconception in Elevator Kinetic Energy Question
I recently encountered the following question in a physics entry test exam:
Question: A man standing in an elevator at the third floor of a building. ...
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Calculating distance between two trains [closed]
Two trains A & B of length 400m each are moving on two parallel tracks with a uniform speed of 20ms-1 in the same direction, with A ahead of B. The driver of B decides to overtake A and ...
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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 ...
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How to calculate angular and linear components of a force acting upon a 3d object?
apologies if this isn't worded great: I don't know all the technical terms for what I'm describing.
Given a 3D object in space (no gravity or air resistance or anything), let's say its center of mass ...
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Deriving the fact that an approximately parabolic terrestrial trajectory is a tiny section of an ellipse
Given that $$|\vec{g}|=\frac{GM}{|\vec{r}|^2}$$ and $\vec{g}$ always points to the Earth's center of mass, can the "almost parabolic" elliptic trajectory be derived provided the initial ...
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Which derivative of position as function of time can be constant in uniform circular motion?
As I understood, the x-t graph for uniform circular motion is sinusoidal, v-t is cosinusoidal, a-t is also cosinusoidal. Is there any futher derivative that is constant throughout each revolution?
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Clarification on Momentum vs Inertia in Exerting Force when Stopping
I encountered a physics question in an exam four years ago that I believe may have had an incorrect answer key. I'm seeking clarification on the correct concept.
The question was:
The property of ...
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Instantaneous velocity in uniform circular motion [closed]
instantaneous speed is the magnitude of instantaneous velocity. if instantaneous velocity becomes zero then it instantaneous speed will also be zero. also, instantaneous velocity is slope of ...
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Doubt about Polar coordinates
I know that for motion that does not involve rotation relative velocity of a object say $a$ with respect to $b$ can be calculated as $$\mathbb v_{ab}=\mathbb v_{ao}-\mathbb v_{bo}$$where $o$ is some ...
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Cross Section Formula and Delta Function Identity (Eq 4.77 in Peskin & Schroeder QFT)
In the book, while deriving the cross section formula for particles A and B, a Dirac delta appears in Eq 4.77:
\begin{align}
\int d\bar{k}^z_A \, \delta\left.
\left(
\sqrt{(\bar{k}^\perp_A)^2+(\bar{k}^...
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Are solids with the same density as air possible?
I was recently considering how to keep a super cheap ultrasonic range sensor safe from balls (or blocks, or whatever) going down ramps (or otherwise moving at high speeds) in a physics lab. It struck ...
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Why is the direction of friction inwards in a rotating disc even though there is no motion in the inward direction?
So, I was studying circular motion and I learnt that when an object is placed on a rotating disc, friction acts inwards to provide the necessary centripetal acceleration and facilitates the circular ...
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I have confusion between the concept of distance and displacement [closed]
I can't understand that why do we say that distance is a scaler quantity and displacement is a vector quantity?
Let me give some examples:
$1)$ Shyam is travelling from New Delhi to Mumbai. Now ...
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Decay of a particle with nonzero momentum into 2 particles: Why are there two solutions?
I am trying to solve a decay of a massive particle into 2 massless particles in the lab frame. I am not interested in the typical solution of boosting the system in the rest frame of the parent ...
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Adding equations of motion
Consider an object of (constant) mass $m$ subject to forces $F_i$ where $i=1,\ldots,n$. Now assume $s_i, v_i, a_i$ are the corresponding equations of motion (position $s$, velocity $v$, acceleration $...
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Calculation of displacement field from a strain field
I am trying to calculate the displacement field from a given strain field in 3D. It is quite a cumbersome calculation, as presented in Applied mechanics of solids by Bower;
\begin{equation}
u_i(x) ...
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Does angular absement exist?
Probably a dumb question. I'm a highschool student, and I don't even know if it is even possible to integrate an angle (for reference, I haven't even learnt integration yet at school, my calculus ...
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Is the Doppler Effect for sound waves with a moving source due to the fact that the wave speed is independent of the source?
The Doppler Effect is typically formulated as follows:
$$f' = \dfrac{v \pm v_o}{v \mp v_s} \cdot f$$
The reason for the frequency increasing for observer moving towards source seems clear enough. It ...
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The No Slip/Slip Condition for Rotating/Rotating and Translating Bodies
Consider a sphere of radius $r$ that is rolling on a rough surface, where its translational velocity $v$ is equal to $\omega r$, where $w$ is the angular velocity of its rotation. In this case, I ...
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Energy in projectile motion
When approaching a projectile motion problem using the conservation of mechanical energy, why do we use the speed of the object as a whole and not only the vertical component?
The horizontal motion of ...
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Shifting a relative coordinate system
I've been working on recreating Boston Dynamics' Spot for the past few months. After addressing the kinematics, I've encountered a significant issue. The way I've set up the leg positions has severely ...
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How to calculate jerk in uniform circular motion?
We can calculate the centripetal acceleration in circular motion by the equation v^2/r. But how do we calculate the jerk (which is acceleration over time)?
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Vector form of kinematic equation for motion with constant deceleration
Here is the equation for finding the velocity in the case of constant acceleration:
$$\vec{v} = \vec{v_0} + \vec{a}t$$
Hence by integrating this equation with respect to t, we obtain position equation:...
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Please help find my error in comparing two acceleration equations
Please help me figure out where my mistake is when comparing two acceleration formulas and coming up with $4x^2 = x^2$. Thank you in advance.
The Kinematic Equations say:
$v^2 = v_0^2 + 2aΔx$
$Δx = ...
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Question regarding $dv/dt =$ Tangential acceleration during circular motion [closed]
During Circular motion or really, any kind of motion it is said that $\frac{d|\vec{v}|}{dt} = |\vec a_{tangential}|$ why is it so?, suppose a particle performing circular motion is moving with ...
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How acceleration affects velocity?
I understood that the acceleration changes the velocity and the velocity changes the position.
So I tried to calculate the position of a falling object, where $y_{acc} = 9.81$ and the initial values ...
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Why is the derivative of the distance between two points not their relative velocity?
I have a problems where I wish to calculate the relative velocity between two objects, and the answer to the problems says that a component of the velocity is second order and hence can be dropped. ...
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How does a sphere roll on ground, no really?
Everyone knows this right!
Consider the ground to be the $xy$ plane and consider gravity to be acting along the $-z$ direction. If a sphere (mass $M$, radius $R$) is placed on the ground and given ...
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Do these two refer to the same reference frame? [duplicate]
What exactly is the difference between a reference frame and a coordinate system (with respect to classical mechanics only)?
Can we claim that these two coordinate systems is from same reference frame?...
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Spinning top moving in curved spacetime
If I have a spinning top in empty space, it would take work to change the orientation of the angular momentum vector of the top. Suppose I throw a spinning top in flat space such that the direction of ...
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Spinning mass around Spring with gravity
I've seen similar posts, but none in which a mass rotates vertically while connected to a spring, with gravity acting on the mass. I want to know if the path of the mass can be described with ...
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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, ...
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How do I know if a motion is 1 dimensional or 2 dimensional?
If an object is moving in a straight line with an angle with x axis (it may be vertical or horizontal) , is it 1 dimensional or 2 dimensional?
The question was asked by my teacher and he himself gave ...
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Draw the angle graphically [closed]
Hi everyone (sorry for the "unclear" title), I'm having trouble graphically representing the point of this:
A stone is thrown from the top of a tower with $h = 50\text{m}$ and with a ...
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Work Done by kinetic friction in Circular Motion
We know when an object is moving in a circular motion on a rough horizontal surface, direction of kinetic friction is constantly. Thus, fto calculate the work doen by friction, we need to use ...
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Is the answer given in the option wrong? [closed]
The question is
"An Object moves along a straight line. The graph illustrates how the acceleration of the object changes with time. The direction of the motion of the object changed only once, ...
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Strain energy stored in a bungee cord pulled at its midpoint [closed]
A bungee cord that behaves elastically has an unstressed length $L=.76$ m and a stiffness $k=140$ N/m. The cord is attached to two pegs, distance $b=.38$ m apart, and pulled at its midpoint by a force ...
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What does it mean when vector quantity is negative?
I’ve seen in some problems that vector quantity is negative. For example, negative Coulomb means that two charges attract… negative acceleration means that object is slowing down. However, magnitude ...
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Motion of person in bus in inertial and non-inertial frame
A person is sitting in a bus that is moving with constant velocity, due to friction their is no relative velocity between bus and the person.
Suddenly the bus starts to move with a constant ...
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Interpretation of a motion in continuum mechanics with a spatial description
in the book introduction to continuum mechanics 4th edition (Michael Lai, second chapter), there is an exercice about a motion of a continuum (exercice 3.2.1).
the motion is $$x1 = X1 + k.t.X2 ;$$
$$...
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What is the correct way to think of position?
How accurate would it be to think of position (along some axis) as the component of radius vector. Example:
$$ \textbf{r} = x \hat{\textbf{i}} + y \hat{\textbf{j}} $$
And if that is correct, we could ...
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How to calculate the relative speed when three bodies are involved? [closed]
Two trains A and B start from a station and move in parallel tracks with velocities 40 kmph and 60 kmph respectively. A man sitting in train A. watches a lady who walks inside the train B at a speed ...
