All Questions
Tagged with kinematics classical-mechanics
255 questions
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Acceleration: Value Disparity?
If we consider a ball moving at an acceleration of $5\ \mathrm{m\ s^{-2}}$, over a time of 4 seconds, the distance covered by the ball in the first second is $5\ \mathrm m$. In the 2nd second will $5\ ...
- 383
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Elastic potential energy in vertical simple harmonic motion
When we calculate gravitational potential energy, we use a reference point as a zero-line. That is, we set the gravitational potential energy to zero at a specific point (usually the ground). Now, ...
- 71
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1
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71
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Relation between fixed constraints and time derivative of the Lagrangian
I have had some trouble interpreting and proving the following statement from Fasano, Marmi's "Analytical Mechanics" (page 139):
"... ${\partial L}/{\partial t} \neq 0$ (1) only if the ...
- 402
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2
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461
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Lagrangian Dynamics of an inverted Spherical Cart Pendulum
Introduction
I have to come up with a PD-controller for an inverted Spherical Cart Pendulum, therefore I tried to compute the Dynamics of such a Pendulum.
The Spherical Cart Pendulum is a hybrid ...
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1
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450
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Is a reasonable assumption to consider that the contact point of the Euler's Disk (with stationary center of mass) trace this finite bounded spiral?
Is a reasonable assumption to consider that the contact point of the Euler's Disk (with stationary center of mass) trace this finite bounded spiral?
This question is highly related to working with the ...
- 103
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4
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358
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How to find motion equations using energy and angular momentum? [closed]
I'd really appreciate some help with an exercise.
The exercise presents a system of two bodies, $m$ and $M$. Both are connected with a weightless rope; the former is rotating (with a given initial ...
- 11
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1
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87
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Finding the angle required to hit a stationary target [closed]
Ignoring air resistace, I have that the height of our canon is $8.2$m and the height of the target is $6.34$m. And that our initial veocity $v_0=18$m/s. I have to determine a way to find the angle ...
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241
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Tilting a water glass so that you can run faster without spilling water (counter-diabatic driving Hamiltonian)
In this paper, there is an interesting figure:
Every attempt I've made to search online to confirm whether or not waiters/waitresses actually do this, has been unsuccessful.
Is there really an ...
- 324
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832
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Inertial Torque Exerted By Engine on Crankshaft
In Shigley(5th Edition), in Chapter 14. Dynamics of Reciprocating Engine ,Section 14.7 Inertia Forces,
the inertia torque exerted by the engine on the crankshaft is given as
$$
\mathbf{T}_{21}^{\...
- 21
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58
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Does super position precede physical phenomena?
If a traveling wave has amplitude of d, it feels certain amount of force at that moment in time when it is displaced for equilibrium. Thus there is also strain on the string corresponding to that ...
- 434
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343
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Smoluchowski theory of Brownian Motion
I am studing Brownian motion, in particular I am reading the book "Brownian Motion, Fluctuation, Dynamics and Application" by Mazo. Now I am dealing with Smoluchowski theory, but I am having some ...
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Calculating velocity of a car based on engine power
Is it possible to calculate the velocity of a car accelerating from rest at full capacity given the power of the engine and the mass of the car? I have a method of solving the velocity with respect to ...
- 1,416
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2
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472
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Impulse Equations
A solid sphere of mass $m$ rolls without slipping on a horizontal surface and collides with a vertical wall, elastically. The coefficient of friction between the sphere and wall is $\mu$. After the ...
- 141
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1k
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Work done: kinetic energy or area under F-ds curve?
Starting from $$F=ma = m \frac{dv}{dt} = m \frac{ds}{dt} \frac{dv}{ds} = m v \frac{dv}{ds}, $$ leads to work done = integral of F.ds = integral of mvdv = change in KE.
Suppose a variable force is ...
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Conservation of linear momentum magnitude along a trajectory
I was once criticized for "taking angular momentum as momentum going
in a circle". I was loosely trying to state, in classical mechanics,
that in using conservation of momentum, one can switch between ...
- 3,808
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How to calculate pressure exerted on the wheels of a robotic car?
I need some help in designing my robotic car. So its going to have 4 wheels, each driven by a 12-volt motor. It occurs to me that the weight of the chassis itself will exert some pressure on the ...
- 219
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Violation of conservation of energy [duplicate]
Sand runs from a hopper at a constant rate $\frac{dm}{dt}$ onto a horizontal conveyer belt driven at a constant speed $v$ by a motor. The power needed to drive the belt can be calculated as follows:
...
- 109
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63
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Determining the trajectory of a particle given the tangential and normal accelerations
Consider a particle with tangential and normal accelerations $\vec{a_T}(t)$ and $\vec{a_N}(t)$ respectively ($t$ is time). If the initial velocity and position vectors are both $\vec{0}$, how can the ...
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29
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Explicit Example of Computing the Action [closed]
I have been dealing with this problem for awhile and I have almost given up. I am asked to compute the action for a free particle going from $x = x_0 = 0$ at time $t = t_0=0$ to its end point $x = x_1 ...
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55
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Relating speed of a flywheel to speed of a shot-out ring [closed]
Let's say I was shooting a 6 lb/cu ft foam ring with an inside diameter of 3 inches and an outside diameter of 5 inches using a flywheel like this:
where s is the distance between the wall on the ...
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1
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46
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Linearly Interpolating in a Non-Inertial Frame
I am working on an engineering task where we have a flying object which knows its height above a curved surface as well as how close it is to other flying objects. If I want to interpolate between two ...
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59
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Statistical Analysis of motion under central force
My question is very simple. If we were to plot the motion of a particle inside circular walls governed by a central attractive force with perfectly elastic collisions, would the statistics of the ...
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113
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If hypothethically a car tries to go in two different directions at the same time, which direction will it end up going?
When we add two vectors(A and B), we get one resultant sum vector(C).
i.e. adding two different directions gives us one resultant direction.
So in the same way if a hypothetical car was trying to go ...
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136
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Difference between eigenvalues of the potential energy Hessian vs. "generalized" eigenvalues with respect to a kinetic energy "metric"
Simple version
Consider if we have a Lagrangian defined by
$$L(q,\dot{q}) = \frac{1}{2} g_{ij}(q) \dot{q}^i \dot{q}^j - U(q) \tag{1a}$$
where the potential energy $U(q)$ has a single minimum at $q=0$ (...
- 3,780
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153
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Finding The Trajectory of particle Kept on a rotating surface
Suppose we "Keep" a particle on a circular, rotating turn-table, rotating with constant angular velocity $\dot{\theta}$, (i.e, the at $t=0$,when the particle makes contact with the table, the ...
- 1,325
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76
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Determining acceleration in order to meet a space-time-velocity reservation
An Example
A train on a single line track is told to be at position $x_{res}$, at time $t_{res}$, and to be moving at exactly $v_{res}$ when it hits that point. Where $_{res}$ denotes the reservation....
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54
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How to accurate scale start velocity in projectile motions? [closed]
I have projectile motion where the angle $\alpha$ is $45^\circ$, and the start velocity is $45\ \rm{m/s}$. We can then expect it to land about $206.422\ \rm m$ away; however, if I were to change/...
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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 ...
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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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86
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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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213
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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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1k
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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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405
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Objects falling on Slopes [closed]
An object falls on a slope and then rebounces....and it is known it hits the slope again...how do I calculate it's second point of contact with the slope....how can a projectory equation be used in ...
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59
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One dimensional motion with changing acceleration. Falling to a large body from a great distance [duplicate]
Possible Duplicate:
Radial fall in a Newtonian gravitational field
My math and physics are rusty. I am trying to calculate the time an object takes to fall to a large body. Before you answer $1/...
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1
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37
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Determine the velocity by a projectile motion [closed]
A snowball rolls from the roof of a large barn that has a downward slope of 20 °. The roof end is 15.0 m above the ground and the snowball has a speed of 6.00 m / s when abandoned from the roof. At ...
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3
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How is final velocity negative when acceleration is in positive direction?
When a body starts from rest and starts accelerating in positive direction and moves certain positive distance, its final velocity is given by :
$$v^2 = u^2 + 2as$$
Solving it gives two values of $v$, ...
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5
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1k
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Do released objects take the direction and speed of their parent frame's velocity, or just the parent frame's speed component?
Context: I'm working on a space game. I noticed that an unpowered object fired from a strafing spaceship appeared, as the released object moved, to curve in the direction the ship was strafing. This ...
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2
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77
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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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In a 2D problem with a thrown object, why is the acceleration along the x-axis equal to 0?
I'm starting Physics, and I don't understand why the acceleration along the x-axis is zero for an object thrown near the surface of the Earth. This may be problem specific, but I wouldn't know since I ...
- 101
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434
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Integrating Angular Velocity Vector using Rodrigues' Rotation Formula
My understanding is that Rodrigues Rotation Formula can be used to explicitly compute an exact rotation associated with a constant angular velocity vector over a given time step.
How do you derive the ...
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212
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Query into the cumulative velocity of mounted platforms
Consider throwing a stone at an object from rest, it travels at Vms-1. Now throw that stone whilst running at Ums-1. It seems in the latter scenario the total speed of stone is V + U. Now imagine ...
- 227
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54
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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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4
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213
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Why acceleration is not always parallel to velocity but velocity is always parallel to displacement? [closed]
Velocity is derivative of displacement :
$$\vec v=\frac{\mathrm {d\vec r}}{\mathrm dt}$$
And acceleration is derivative of velocity.
$$\vec a=\frac{\mathrm {d\vec v}}{\mathrm dt}$$
Given that their ...
- 325
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55
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Is the way of determining my angle of vector wrong or am I using the wrong formula for calculating magnitude of resultant? [closed]
i) Two balls A and B are simultaneously projected from top of building at 10m/s upward and 20m/s downward. Find distance between them after 3s? (Answer: 90m)
There are two magnitude of resultant ...
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60
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When does a free body moving on a smooth circular path make a complete revolution?
If we have a body like the one below , What will be the minimum initial velocity $V_0$ to complete one revolution, My assumption was that it has to reach $\theta=180$ ,But how do I describe this ...
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1
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35
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Displacement on trip around globe?
I am tutoring in physics, specifically in kinematics and uniform acceleration, and I thought it would be fun to find the time it would take for a car to drive around the globe given an initial ...
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2
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112
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How is energy conserved in terms of "Work"
Basic equation of work is given by $F\cdot s$. When work is done, the energy is stored either in form of potential or kinetic. My question arises when we look at a case of applying $m g$ of force ...
- 434
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384
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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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2k
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6 Story Building Swaying, Normal? [closed]
Preface:
I'm currently sitting at my desk on a 5th floor in a South Florida office building, as I was earlier this morning when I felt the building sway slightly. It wasn't continuous and the ...
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