Newtonian mechanics covers the discussion of the movement of classical bodies under the influence of forces by making use of Newton’s three laws. For more general discussion of energy, momentum conservation etc., use classical-mechanics, for Newton’s description of gravity, use newtonian-gravity.

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What happens when the spacecraft velocity equals the velocity at it's exhaust?

So there I was resting me eyes thinking about rocket drives, and what-not. The thought struck me that, perhaps, even before Mr. Einstein interferes with the increasing velocity of the spacecraft Mr. ...
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289 views

What are the reasons for leaving the dissipative energy term out of the Hamiltonian when writing the Lyapunov function?

I have a problem with one of my study questions for an oral exam: The Hamiltonian of a nonlinear mechanical system, i.e. the sum of the kinetic and potential energies, is often used as a Lyapunov ...
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Direction of rotation of a celing fan

From Constellation Energy Quick energy efficiency tip: To stay cool and manage your energy at the same time, use ceiling fans to create a “wind chill” in rooms you are using. The wind chill ...
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1answer
313 views

Shaping a wire such that a bead sliding on it has exactly isochronous oscillations

Let a wire be shaped according to some even function $y=f(x)$, with $f'(0)=0$ and $f''(0)>0$, and let a bead of negligible size slide frictionlessly on the wire. Let the bead oscillate ...
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Simple friction formula for a car

I am making a 2D driving video game, and I would like to know the "simple" formula for calculating the friction force between the car and the road. I have read lots of friction diagrams involving ...
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1answer
127 views

Velocity distribution in Plummer's models and others mass distributions

The Plummer's sphere is an model for the mass density in a globular cluster of stars. For an $N$-body simulation I have initialized the position of $N$ masses with a Monte-Carlo technique but cannot ...
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2answers
114 views

Why isn't the product rule used in the definition of mechanical work?

Mechanical power is normally defined as $P = \mathrm{d}W/\mathrm{d}t$, and work is normally defined as $W = \vec F \cdot \vec x$. Today an undergrad pointed out a confusion he had from Griffiths' ...
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How Felix Baumgartner has reached the speed of sound quickly

I have watched Felix Baumgartner freefall; but I wonder how Felix has reached the speed of sound quickly, in a matter of some seconds, then we had no idea of its speed? Any explanation please.
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2answers
368 views

How much thrust would be needed to turn a hobbyist weather balloon into a deep space probe?

I was reading the article Weather Balloon Space Probes that says you can put your own balloon probe at 65,000 ft temporarily. Is it even remotely possible to raise the probe high enough using ...
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2answers
178 views

Strong Newton's third law of action and reaction: Mathematical Interpretation

According to the strong law of action and reaction for internal forces(Goldstein): "$F_{ij}=-F_{ji}$ and the forces lie along the direction joining the particles." Now consider the statement If ...
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2answers
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Orbital speed for a circular orbit?

I wanted to look up the formula for orbital speed for a circular orbit on Wikipedia, and I found 2 formulas: All bounded orbits where the gravity of a central body dominates are elliptical in ...
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3answers
303 views

Are elliptical orbits really elliptical?

I have wondered for a long time how elliptical orbits can work. It seems awkward for a freely-moving object to come very close to a source of gravity and then return to the exact point where it ...
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359 views

Does the law of Universal Gravitation apply to every matter?

If I have a big ball of 20,000,000kg and another of 100g, does it mean that the big ball will pull the small ball towards it?
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2answers
226 views

How to reconcile the two definitions of work? (mechanical and thermodynamical)

When studying classical mechanics, work is defined as: $W_M=\int F_{tot} \hspace{2 mm} dx$. However, for thermodynamics, work is defined as: $W_T=\int -F_{ext} \hspace{2 mm} dx$. I'm having trouble ...
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2answers
177 views

Extension to continuous in proofs of rigid body mechanics

I'm studying rigid body mechanics and I've seen several proofs of properties related to total angular momentum, kinetic energy, etc. that all regard discrete set of points. For example, to show that ...
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1answer
102 views

Boundary conditions on wave equation

I am having trouble understanding the boundary conditions. From the solutions, the first is that $D_1(0, t) = D_2(0, t)$ because the rope can't break at the junction. The second is that ...
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2answers
733 views

Finding optimal angle for projectile, taking into account linear (Stokes) drag

If you throw a projectile from the ground at a certain angle, it's not hard to see that, assuming we're in a vacuum, throwing it at 45º from the ground will always make it go farthest before it hits ...
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2answers
2k views

block slides on smooth triangular wedge kept on smooth floor.Find velocity of wedge when block reaches bottom

Find the velocity of the triangular block when the small block reaches the bottom: Here is what I did: The final velocity(at the bottom)of the small block of mass m is $\sqrt{2gh}$ along the plane ...
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2answers
839 views

First and Second Moment of Mass

I recently came across the definition of the Center of Mass of a system as the point about which the first moment of mass is zero. Further, it defined Moment of Inertia as the second moment of mass. ...
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Does Earth's Rotation Affect Its Shape?

The question I am working on is, "Consider the following. (a) Find the angular speed of Earth's rotation about its axis. rad/s (b) How does this rotation affect the shape of Earth?" I am fully ...
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777 views

Newton's 3rd Law: How can I break things?

If I punch a wooden board hard enough and it breaks in two, has the board still exerted a force of equal magnitude on my fist? When the board breaks in two due to my force, the halves have a ...
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2answers
1k views

First integral of an equation of motion: $\mu\ddot r=-\frac{k}{r^2}$

I've got an equation of motion (EOM), which is $ \mu\ddot r=-\frac{k}{r^2} $ How do I find the first integral of this EOM? I'd appreciate it if someone could show me the steps involved. I should ...
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1answer
284 views

What is the function of the top point of a bouncing ball?

A ball is thrown away as parallel to x axis from M(0,h) point with speed V . After each jumping on x axis , it can reach half of previous height as shown in the figure.(Assume that no any air ...
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0answers
120 views

Equation of motion for a falling rod (with one end touching a frictionless surface)

I have a quick question about the equation of motion for a falling rod (with one end touching a frictionless surface). The end touching the surface is not fixed. I am given the moment of inertia about ...
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2answers
152 views

Rod Falling on Frictionless Surface

A rigid rod with mass m is initially held at an angle with respect to a frictionless plane by a string. Then the string is cut. What happens to the rod? My intuition suggests that the rod should slide ...
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2answers
176 views

Rocket/Thrust/Gas/Free Expansion of Gas

We know, the rockets in space use Newton's 3rd law to increase their velocity and hence move. What I don't understand is how it is possible in space aka vacuum-state without air? From what I know, ...
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2answers
160 views

Centripetal force in frame of reference of body moving In a circle

Suppose a body is moving in a circle about a fixed point. In the frame of reference of the body, is the centripetal force felt or is only the centrifugal force felt? More generally, does a body only ...
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177 views

Loop-the-Loop with Friction [closed]

Let's consider a track that begins vertically becomes a 450 degree loop, and level off. (See diagram) We drop a block from height $H$ that falls and goes around the loop. Ignoring air resistance, ...
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2answers
198 views

Mathematical model for this graph of a simplified binary star system?

Unnecessary background for question: I had a school assignment asking us to relate a quadratic equation to a real life example relating to our future dream career, making sure to express the accuracy ...
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1answer
112 views

Does a 27 hp engine output the same amount of energy as lifting a 1 ton stone block almost 3 meters per second?

I’m trying to get a sense of how much energy a 27 horsepower engine outputs. 27 hp $=$ 20 133 watts (joules/second). Potential energy can be calculated as $E = mgh$ where $g = ~9.8\ m/s^2$ on earth. ...
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2answers
108 views

Path of Orbital Bodies

I am trying to figure out how to parametrize the path of a body under the influence of gravity from another body, but I am stuck. I have looked at the Wikipedia page on Kepler orbits, but it is ...
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284 views

Determination of mass density distribution of an object

This is a follow-up to a previous question How can you weigh your own head in an accurate way?. My purpose is not to restart the flurry of more or less humorous jokes (which are not such a bad thing ...
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1answer
287 views

What if exactly half the Earth's population jumped at one instant? + Secondary Question

I read somewhere that when you jump, the sole effect caused by your jump on the earth moves it about $10^{-18}m$ (I don't remember the figure exactly, but I think it was that). However - obviously ...
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Cylinder rolling down an inclined plane

I've been trying to solve this problem: A cylinder is rolling down an inclined plane (angle between plane and horizon α). Coefficient of friction is µ. What is the translational and angular speed of ...
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2answers
60 views

Velocity in a turning reference frame

I often see the relation that $\vec v=\vec v_0+ \vec \omega \times \vec r$ in a turning reference frame, but where does it actually come from and how do I arrive at the acceleration being $$\vec ...
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280 views

Movement of man and ladder and their center of mass

Suppose there is a massless frictionless pulley. A rope over it carries a mass $M$ and on other side carries a ladder of mass $(M-m)$ and a man on that ladder, of mass $m$. Now the man starts ...
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2answers
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Fictitious forces confusion

I have a hard time understanding the subject of fictitious forces. Let's discuss a few examples: 1) I'm sitting inside a vehicle which is accelerating in a straight line. I feel like someone is ...
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1answer
2k views

Determine acceleration from experiment (Newton 2nd Law)

I have done a physics experiment (setup below). And was asked to determine the experimental and theoretical acceleration. The data I've got Ok, am I right to say Experimental acceleration ...
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321 views

What sustains a rigid body's rotation at its constant angular(rotational) speed?

Continuing from the following scenario from my previous question Centripetal force of a rotating rigid body? : Consider someone pushing a roundabout in a playground. Initially the roundabout is ...
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Earth-Centered Inertial (ECI) reference frame as approximate inertial frame of reference

In many practical applications, one can consider the Earth-Centered Inertial (ECI) reference frame approximately as an inertial reference system, though strictly speaking, it is non-inertial. Is ...
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Why did they add a Centripetal Force in the Free-Body Diagram?

problem ! solution ! Why do they have the centripetal force in there? I understand that the normal force is the centripetal force here, but why would they say "or $\frac{mv^2}{r}$"? I thought it ...
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4answers
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What is the difference between a moment and a couple?

In mechanical engineering, the torque due to a couple is given by $\tau = P\times d$, where $\tau$ is the resulting couple, $P~$ is one of the force vectors in the couple and $d$ is the arm of the ...
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3answers
260 views

How long does it take for an electric car to go from 0 to 60 mph?

I found the freefall motion equation which describes terminal velocity of a falling body, but I can't find a similar equation for a vehicle subject to constant traction force, so I tried determining ...
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2answers
61 views

Ice throw from industrial wind turbine

I was watching a documentary where the residents didn't want to have a wind turbine erected nearby. One of the comments from the company was that an ice throw would have very little importance since ...
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1answer
105 views

Free fall time with non uniform acceleration and some initial velocity

Free-fall time for two objects on a radial path (starting from rest) is given by: $t(y)=\sqrt\frac{y_0^3}{2u}\biggl(\sqrt{\frac{y} {y_0} \bigl({1} -\frac{y}{y_0}}\bigr) + ...
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What is the third law action pair of buoyancy?

Consider a block floating in a fluid. The force due to gravity balances the buoyant force exerted on the block. But there must be a third-law action pair to the buoyant force. If the block exerts a ...
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Force when acceleration is zero

i tried to find it in books but i was unable to do so and i am not able to understand this and I couldn't think of a better example. i repeat. its just an example. if i punch someone's face with my ...
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Did relativity make Newtonian mechanics obsolete?

Did Einstein completely prove Newton wrong? If so, why we apply Newtonian mechanics even today? Because Newton said that time is absolute and Einstein suggested it relative? So, if fundamentals are ...
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110 views

Centre of instantaneous rotation problem

Is there a point of Centre of Instantaneous Rotation (CIR) for every type of motion or only for cases of rolling?
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175 views

Increase in velocity by loss of mass? [closed]

A trolley of mass 300kg carrying a sand bag of 25kg is moving uniformly with speed of 27km/h on a frictionless track. After a while, sand starts leaking out of a hole on the floor of the trolley at ...