All Questions
105 questions
2
votes
2
answers
224
views
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 ...
- 213k
2
votes
4
answers
1k
views
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 ...
CommunityBot
- 1
0
votes
2
answers
54
views
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 ...
- 99.9k
0
votes
1
answer
43
views
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 ...
- 956
1
vote
3
answers
82
views
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 ...
- 5,831
-4
votes
3
answers
92
views
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 ...
- 3,062
2
votes
0
answers
80
views
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
views
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 ...
- 778
0
votes
1
answer
94
views
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 ...
- 3,303
0
votes
1
answer
138
views
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 ...
- 1,262
2
votes
2
answers
281
views
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 ...
- 1,350
0
votes
1
answer
97
views
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 ...
- 12.9k
0
votes
0
answers
31
views
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
1
vote
0
answers
44
views
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:
...
- 378
1
vote
0
answers
29
views
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 ...
- 923
0
votes
2
answers
239
views
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 ...
3
votes
1
answer
241
views
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 ...
CommunityBot
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0
votes
2
answers
434
views
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 ...
- 12.9k
1
vote
1
answer
59
views
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 ...
- 48
0
votes
0
answers
73
views
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
0
votes
2
answers
60
views
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 ...
- 2,183
0
votes
1
answer
87
views
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 ...
- 401
1
vote
5
answers
7k
views
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 ...
- 222
0
votes
2
answers
232
views
Kinematics of particles
Do particles have to move in a straight line to apply Suvat equations?
I always perceived that they do because acceleration can mean a change in the magnitude of velocity, a change in direction or a ...
CommunityBot
- 1
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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-1
votes
1
answer
71
views
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 ...
- 1,406
0
votes
1
answer
35
views
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 ...
- 39k
2
votes
1
answer
167
views
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 ...
- 347
0
votes
2
answers
94
views
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 ...
- 277
0
votes
3
answers
238
views
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 $0$ ...
- 3,345
1
vote
2
answers
227
views
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/...
- 728
-1
votes
1
answer
83
views
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 ...
- 28.4k
7
votes
4
answers
633
views
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 ...
- 3,405
-8
votes
2
answers
218
views
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 ...
- 109k
2
votes
3
answers
721
views
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 ...
CommunityBot
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1
vote
1
answer
141
views
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 ...
- 12.9k
2
votes
1
answer
582
views
Motion equations for Woodpecker toy (multibody system)
I am trying to understand a rigid multibody model of a Woodpecker toy (see figure below). Now I am not going to go into details about the model or justify this approach, I am just trying to understand ...
- 2,666
0
votes
1
answer
187
views
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 ...
- 22.5k
-2
votes
1
answer
116
views
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 ...
- 24.7k
0
votes
2
answers
58
views
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 ...
- 77.9k
1
vote
1
answer
86
views
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 ...
- 109k
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 ...
- 12.9k
0
votes
1
answer
46
views
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 ...
- 708
5
votes
2
answers
2k
views
Rigid body dynamics joints
I can't seem to find any info on connected rigid bodies by a joint. Can someone explain the basics to me? I'm trying to do a little research to find out how feasible it would be to implement 3d ...
- 2,666
1
vote
1
answer
153
views
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 ...
- 12.9k
1
vote
1
answer
241
views
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
1
vote
2
answers
2k
views
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 ...
- 8,040
1
vote
2
answers
113
views
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 ...
- 1,076
0
votes
2
answers
97
views
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 ...
- 8,476
-2
votes
1
answer
87
views
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 ...
- 213k