19 votes
Accepted

Is there an explanation for action-reaction law?

Yes, the explanation is the conservation of momentum. In Newtonian mechanics the third law produces conservation of momentum in mechanical systems. Later on you will see cases (matter interacting with ...
  • 70.9k
6 votes

Number of integrals of motion

Every autonomous dynamical system arising from mechanics can be described as a first-order ODE on a $2n$-dimensional manifold $M$ (the spacetime of kinetic states of Lagrangian mechanics with local ...
5 votes

Why does particle leave circular motion after string slacks?

Gravity governs projectile motion, so it is still accelerating the object downwards. The velocity at the time of exit is that it had at some point in the circle, which, instantaneously, was tangent to ...
4 votes
Accepted

Is the normal force the reaction force?

There are two different third-law force pairs. One pair is the downward gravitational force on the box and the upward gravitational force on the earth. The other is the upward normal force on the box ...
  • 19.2k
4 votes

What is the velocity of centre of mass in centre of mass frame?

In the absence of any external forces, the velocity of the center of mass is constant in any inertial reference frame. The particular constant will depend on the reference frame. On the center of mass ...
3 votes

Force and momentum, cause and effect, transition and state

The symmetry of the interactions is the cause for the observed effect that the momentum change is zero. There is no cause and effect relationship here. The symmetry and the conservation law have a ...
  • 70.9k
3 votes

Is the normal force the reaction force?

The best way to visualize and solve force problems like this is with a Free Body Diagram, in which you isolate each body and draw all forces acting upon it. That way it is easy to see what forces are ...
  • 3,685
3 votes

How do I convince my students the Newton's first Law is the way it is?

You might try giving them a lesson on the history of physics. Where did Newton's first law come from? Well, it came from a series of experiments performed by Galileo. In those experiments he let a ...
  • 20.8k
3 votes

Does an inertial frame have to be orthogonal?

You can set up whatever co-ordinate axes you like in an inertial frame of reference (or, indeed, in a non-inertial frame of reference) - orthogonal, non-orthogonal, cylindrical, spherical etc. What ...
  • 36.6k
2 votes

Does a slow moving object fall faster than a fast falling object?

Velocity is not the only factor that determines the drag force. Area of cross section, for example, is another factor affecting the magnitude of drag. If everything else is same except the velocity, ...
  • 100
2 votes

Confusion regarding work done by external force

Now, let me apply an external force on the ball in the midst of its journey which is equal and opposite to the force of gravity. First of all, the external force you need to apply has to keep ...
  • 58.3k
2 votes

Force and momentum, cause and effect, transition and state

Can one in good faith say "forces oppose each other because of the fundamental axiom that momentum is conserved", instead of the other way around? Are the two sentences equivalent? That ...
  • 39.6k
2 votes

How do I convince my students the Newton's first Law is the way it is?

Newton's first law is, unfortunately, not a trivial proposition. What it tells us is that there are inertial systems in which the motion of objects is, as my high school physics teacher put it, "...
2 votes

Doubt regarding spring block system

Your statement . . . . . hence when it will be released,it will have an initial velocity $\bf v$ is incorrect and it should read . . . . . when released it will have an initial velocity of $\bf zero$? ...
  • 80.9k
2 votes
Accepted

Doubt regarding spring block system

We use work energy theorem when the block is at the right extreme. Your equation is incorrect. It should read $$\int_{-x}^{0} kx\mathrm{d}x+\int_{0}^{x} -kx \mathrm{d}x=0\tag{1}$$ Because the initial ...
  • 58.3k
2 votes

Doubt regarding spring block system

First of all, the work done by the spring is simply $\int_{x_i}^{x^f} k x dx$. Second, your initial velocity is zero. In the first half of the full swing (from $x=-|x_0|$ to $x=0$) the spring performs ...
  • 224
2 votes

Does an inertial frame have to be orthogonal?

I think your question actually is: Should the basis vectors of a coordinate system be orthogonal? The answer is no, you can choose the basis vectors in any way you would like. An inertial frame ...
1 vote

I have designed a 3D gyro but what can I expect after I produce it?

General rule for rotor design: for a given weight of the rotor try to put the mass towards the rim. That is: make most of the rotor thin, as thin as possible while still providing sufficient ...
  • 16k
1 vote

Calculating spring forces, when springs are angled

With the constraint that the spring can only move along its axis, then you need only find the component of the force in the direction of the axis. The normal force of the ground acting on the wheel, ...
  • 11k
1 vote
Accepted

Coulomb's law: Is $F_1$ equal to $F_2$ even if $q_1$ is not equal to $q_2$?

As an aside: The force F on an electric charge $q$ in an electric field E is F = $ q $ E. For two charges $q_1, q_2$ separated by a distance $r$ you can think of it in two ways: (1) The first charge ...
  • 3,713
1 vote

Coulomb's law: Is $F_1$ equal to $F_2$ even if $q_1$ is not equal to $q_2$?

Yes. That is from Newton's third law, which is experimentally derived. Equal in magnitude, opposite in direction.
1 vote

How to draw vectors?

For one thing, if $F_x$ and $F_y$ are components of $\vec F$, they are usually drawn not to extend beyond the projection of $\vec F$ in that direction. E.g. the $F_x$ arrow in Fig 1 should be much ...
  • 3,685
1 vote

Why does particle leave circular motion after string slacks?

Answering the second part first: While the force of gravity provides exactly the required centripetal force at the highest point, the force of gravity does not change direction as required for the ...
1 vote

Projectile motion as realistic as possible (at least computationally)

Is numerical integration an option? If so, you can simply start by modelling the projectile as a point mass, and define its initial conditions(mass, position, velocity), and the Net Force that acts on ...
1 vote

Why does particle leave circular motion after string slacks?

Following is not a full answer but a comment to help OP figure out the answer on their own. Gravity does not provide centripetal acceleration to the particle. This is because centripetal acceleration ...
  • 100
1 vote

Why does particle leave circular motion after string slacks?

Why does this phenomenon occur even though the component of weight can provide centripetal acceleration? It occurs precisely because the weight can provide centripetal acceleration. More to the point,...
  • 484
1 vote
Accepted

Speedometer Dilemma

Why is there an x in the speedometer reading in the first portion? A 'speedometer' shows your speed, and if you consider you are moving in whatever the 'forward' direction is, that gives you a ...
1 vote

Two forces act on a body as shown

Length of the arrows proportional to the magnitude of the force, an then draw the force parallelogram or triangle.
  • 4,030
1 vote
Accepted

Relationship between work and potential energy

About the concept of potential energy: Ultimately the basis of the concept of potential energy is the Work-Energy theorem. The starting point for deriving the Work-Energy theorem is Newton's second ...
  • 16k
1 vote

Taking centrifugal insted of centripetal changes friction direction?

In an inertial frame of reference we need a centripetal force to make the car go in a circle instead of in a straight line. Friction provides this centripetal force so it is directed towards the ...
  • 36.6k

Only top scored, non community-wiki answers of a minimum length are eligible