All Questions
105 questions
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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 ...
- 96
0
votes
1
answer
43
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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 ...
- 45
1
vote
3
answers
82
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How much time does it take for an object to fall from space? [closed]
Let's say there's an object of mass $m$ in space, $h$ meters away from the surface of the Earth. $h$ is large enough that $g$ cannot be assumed to be constant. The acceleration varies according to ...
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-4
votes
3
answers
92
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How do you prove the formula for momentum? [closed]
I am just an absolute beginner to physics. I've seen a proof of the formula for momentum using Newton's second law of motion, but to prove Newton's second law of motion you have to use the formula for ...
2
votes
0
answers
80
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Equation of Motion of Rigid Body Represented by Twist and Derivative of Twist
This question is an extension of question Understanding terms Twist and Wrench.
Assuming there is a rigid body with body twist denoted as $\mathcal{V}_{b}=\left(\boldsymbol \omega_{b}, \boldsymbol v_{...
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1
vote
1
answer
182
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Bouncing a ball on an elevator that is ascending
My question may be simple but I'm curious, let's say I start bouncing a ball like a footballer with my foot on an elevator, and it starts moving upwards (with acceleration) and then it stabilises ...
- 45
0
votes
1
answer
94
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Velocity and acceleration of a ball shot uphill [closed]
Consider a ramp of length $100$ m and with a height of $10$ m. At the base of that ramp we're shooting a ball of mass $12$ kg uphill. Let's say the ball has a speed of $1$ m/s at $1$ m uphill. How can ...
- 103
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1
answer
138
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Question about period and frequency
In the context of uniform circular motion, I have been so informed that period ($\tau$) is properly measured in seconds; and that frequency ($f$) in inverse seconds. Why is this the case? Wouldn't the ...
- 197
0
votes
1
answer
97
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Angle, and maximum area of projectile motion accounting air resistance
Recently I was wondering about what will happen to the particle when subjected various elevation angle of projectile motion if we account air resistance. I want to know what the angle of elevation ...
0
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0
answers
31
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What was the professor counting regarding constraint forces? [duplicate]
I am taking a mechanics class at university. Last week we started describing movement over a curve; we are given a natural parametrisation $s(t)$, and then we have the following relations:
$$ \vec{r}(...
- 179
2
votes
2
answers
281
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When a car curves, if friction points towards the centre which force makes the wheel rotate?
The translational motion of the wheel is due to the friction right. If friction is towards the centre during a turn, which provides the translational motion to the wheels? Or is it the component of ...
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1
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0
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44
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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
1
vote
0
answers
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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2
answers
239
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Angle of projection for the minimum time of flight for a given range
If a projectile has to cover a fixed range under gravity, then what should be the angle of projection for the total time of flight to be minimum?
The initial and final point of the projectile are both ...
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0
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73
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Necessary and sufficient conditions for periodic motion
Let us fix a reference frame $S$ with origin in $O$ in the euclidean space $\Bbb R^3$, then let us also define a periodic motion in the following manner:
A motion is periodic if and only if the time-...
- 402
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2
answers
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 ...
0
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2
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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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votes
1
answer
87
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Find the equation for the angle $\theta$ in which the particle leaves the semicircle. No Friction [closed]
I think I missed something in this mechanics problem.
We're given a polished (no friction) and homogeneous hemicircle which has mass $M$ and a particle of mass $m$ laying on the top of it.
There is ...
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votes
1
answer
71
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An easier way for me to calculate the distance , But does it always stand true? [closed]
When can I say that the distance is equal to $d=\int^{t_2}_{t_1}|V|dt$ , Where V is the velocity and it's given in terms of time and $t$ is the time , You might wonder why I'd need this ; it's ...
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1
answer
35
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Question - Maximum range of Ballistic gunshot formula: $V_M=\sqrt{Rg}$
I have a question on physics, broke my head, saw the answer, then I see there is a formula for calculating the distance from the end of the mouth of the rocket to the finish line.
If the length of ...
2
votes
0
answers
183
views
Proving that the relative angular velocity of any particle with respect to any other particle is the same in a rigid body
Claim: The angular velocity of any point mass of a rigid body relative to any other point mass is the same, i.e., $\vec{\omega_{i,j}} = \vec{\omega}\;\,\forall{i}\,\forall{j}$, where $\vec{\omega}$ is ...
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2
votes
1
answer
167
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What is the relationship between the speed of the end of the thread and the angular velocity of the spool which was pulled by the winding thread?
On a rough ground, there is a cylindrical spool of inelastic thin thread (as the picture following), the inner and outer radii are $r$ and $R$ respectively, the thin thread is wound in its inner ...
- 363
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2
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94
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Normal reaction on a mass travelling along a curve
I've come across a set of problems in classical mechanics, where I am supposed to find the value of the normal reaction that acts on a mass, as it travels along a curve $y=f(x)$.
For example, suppose ...
- 1,853
1
vote
2
answers
227
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Force from time and velocity
Let's say I have a goal velocity $(v)$. In $n$ amount of time $(t)$ (let's say two seconds). What is the formula for finding the amount of force I would need (not counting other forces like drag/...
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votes
3
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238
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Equation of motion of a classic inverted pendulum in free fall
I was thinking in this interesting problem:
Suppose we have this inverted pendulum:
But without this control force $F$ and the system would by loose from a height $h_0$, with initial velocity $0$ ...
1
vote
1
answer
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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1
answer
83
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Why does the Normal reaction force vary in a straight line & curved path?
As visible from the above picture, the normal reaction force while ascending on an incline gradually decreases, however for a circular/curved path it increases. Intuitively, this seems wrong to me.
My ...
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7
votes
4
answers
633
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Speed resulting from tangentially applying force to solid spheres with different mass distributions
Given are two solid spheres of the same size and weight. They both have their center of mass at their geometric center.
One of them (A), however, has most of its ...
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2
answers
218
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Infinite Motion from Finite Motion [closed]
By stringing an arbitrarily large number of double-reduction gears together, it is possible to create a system (assuming no gravity and no friction) where the final gear is making an arbitrarily large ...
1
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1
answer
141
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Newton's 1st law, applied in a manifold
A seemingly interesting question.
Newton's 1st law states that objects continue in straight lines, unless acted upon by external forces. Now consider a frictionless manifold. Since it is locally ...
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1
answer
187
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How can the $x$-components of the frictional force and the normal force be the same for a static block on an incline? [closed]
I recently was assigned this problem as part of my homework:
"A block sits on a plane that is inclined at an angle $\theta$. Assume that the friction force is large enough to keep the block at ...
2
votes
3
answers
721
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I am moving right and rain is falling vertically down.Why should I hold umbrella at an angle?
This is related to relative velocity.I get that, from my moving frame of reference rain is making an angle.But still... it doesn't make sense to hold umbrella at an angle when rain is falling ...
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1
answer
116
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Regarding Uniform Acceleration [closed]
Please give some basic intuition or hint to solve this question. I'm getting stuck.
The star of a distant solar system explodes as a supernova. At the moment of the explosion, a
resting exploration ...
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0
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2
answers
58
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Inclined planes and motion [closed]
A particle of mass $2\;kg$ is fired up a smooth slope of length $4 \;m$, with initial speed $10\;m/s$, inclined at an angle $30^\circ$ degrees above horizontal. What is the speed of the particle at ...
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1
vote
1
answer
86
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Exact distance travelled by an object due to gravity only
I am aware of the fact that for two point masses in space, the time that it will take for them to collide is, T=$\pi \sqrt{\frac{r_i^3}{8GM}}$, where M is the sum of the 2 bodies' masses, $r_i$ is the ...
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votes
1
answer
46
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Distance of slowing object [closed]
I have object with a given mass $m$, which is moving with the velocity $v$ and there is force $\bf F$ pushing against movement of the object.
How far will object travel until it stops and how long ...
- 3
0
votes
2
answers
694
views
How to maintain the same initial velocity in trials with projectile motion experiment?
If I would like to experiment with projectile motion to determine the relationship of launch angle and horizontal range (for instance, I would throw a ball multiple times from a height with varying ...
user282164
1
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5
answers
7k
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Optimum launch angle for a projectile launched from a height above the ground [closed]
If a projectile is launched from a height greater than zero and landed to a height equal to zero, is the optimum launch angle that gives the greatest horizontal range still $45$ degrees or not?
I know ...
user282164
1
vote
1
answer
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 ...
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1
vote
2
answers
2k
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Direction of velocity and displacement
Do velocity and displacement always have the same direction? I know this seems like a silly question to ask, but I'm having a hard time coming up with any counter examples, and I'm not able to prove ...
1
vote
2
answers
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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2
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97
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How to decide which velocity is bigger in a collision before writing velocity of approach and velocity of separation?
My teacher said that velocity of separation is $V_1$- $V_2$ where $V_1$ is greater than $V_2$ and said same for velocity of approach. The problem is how would you determine which velocity is greater ...
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votes
1
answer
87
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Why does the radius of curvature is constant in $n$-$t$ coordinate kinematics?
Deriving the relations kinematics on an $n$-$t$ coordinate system is said that if we have a particle $A$,after differential of time $dt$ the particle moves to $A'$. Assuming a curvilinear motion, the ...
0
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2
answers
361
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Why does something thrown out of a train goes in the opposite direction?
As someone throws some thing out of the train in y direction it should move forward (in the direction of the train) in x direction, (wrt ground) as it has velocity component in the direction of moving ...
1
vote
0
answers
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
1
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3
answers
505
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Relative Velocity of two particles [closed]
If two particle are neither approaching towards nor receding away from other then their relative velocity is non zero.
How is this possible??
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2
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1
answer
362
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What is the reactionary force exerted on a swing?
On a playground swing, children quickly learn how to swing higher and higher by timing their body motions with the resonant frequency of the swingset. But it occurs to me that it seems you're making ...
- 2,754
3
votes
3
answers
893
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Newton's Second Law in vertical launch of a rocket
Consider a rocket being launched vertically.
Let $T(t)$ denote the thrust from the engine and $M(t)$ be the total mass of the rocket at time $t$.
At $t=0$, $T(0)=M(0)g$ (so that the normal force due ...
- 1,047
4
votes
1
answer
780
views
Is Centripetal Velocity a Thing?
I'm quite new to physics so this question may sound dumb for many of you. But when I was learning about uniform circular motion, all sources I can find talks about centripetal acceleration, and, when ...
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3
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1
answer
137
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Average Velocity ($\vec{\bar{v}}$) Intuition and Analogy for Non-Uniform Acceleration
Background
So I was trying to make as much sense out of kinematics through intuition after having taken my first semester of university physics, and I've stumbled onto a dillema that I can't seem to ...
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