For a stationary object forces need not be zero, but momentum is zero. Since mass is a scalar quantity and velocity is a vector quantity, we can derive that momentum must therefore be a vector quantity as the product of a vector with a scalar is a vector. This metric is homogeneous and isotropic, which implies 3-momentum conservation. thanks The direction of the momentum vector is in the direction of the body’s velocity. The direction of momentum depends on the direction of velocity. I could ask the same thing about the electromagnetic field tensor, but momentum seems to be a good place to start. Is momentum a vector? @m4r35n357 I'm saying that the canonical momentum of Lagrangian/Hamiltonian mechanics is a one-form, and that using the metric to raise its index gives you its 4-vector partner. Momentum is a vector: It has a direction as well as a magnitude. As discussed in an earlier unit, a vector quantity is a quantity that is fully described by both magnitude and direction. It exists. A car (m1) travels north at a speed of 15 m/s. The standard (dot-product) … Here we will demonstrate the power of 4-vector thinking by deriving the momentum 4-vector, of which the momentum 3-vector is a part. Construction of the Momentum 4-Vector. mass Correct! The direction of force depends on direction of acceleration. Momentum being the product of a scalar quantity and a vector quantity, it is also a vector quantity. Momentum is a vector since it is the product of velocity and mass, therefore impulse must be a vector quantity because the difference of two vectors is still a vector. Momentum of an object is the product of its mass and velocity (p=m x v). African sleeping sickness is due to (a) Plasmodium vivax transmitted by Tsetse fly (b) Trypanosoma lewsii transmitted by Bed Bug (c) Trypanosoma gambiense transmitted by Glossina palpalis (d) Entamoeba gingivalis spread by Housefly. ⃗⃗⃗ = m ∙ Momentum is a vector quantity that has the same direction as the velocity of the object and a magnitude m times the velocity. Questions can be in two (or more) dimensions like this one: (b) The direction of velocity (c) The direction of acceleration. What actually is the vector of angular momentum? Example During this elastic collision the momentum of small … Either that, or we have two distinct geometric objects representing momentum. Is force a contravariant vector or a covariant vector (or either)? One to one online tution can be a great way to brush up on your Physics knowledge. So it's perhaps not surprising that the vector nature of momentum is hard to get hold of from the traditional examples, where momentum is represented as either a positive or a negative number. Generator of translations in classical mechanics. One Dimension. (velocity).-- Velocity is a vector. Intuition behind dual vectors ('Bongs of a bell' does not help). ", My professor skipped me on Christmas bonus payment. So as a differential of a scalar function, momentum is naturally a covector, not a vector. It collides with a car (m2) traveling east at 22 m/s. For that, you'll need to be more specific about what you mean by momentum. So if a vector and its dual 1-form are not to be viewed as different representations of the same object, momentum must be one or the other. The teacher quickly inverts the can containing boiling water into a bowl of cold water, as shown in the diagram. Just checking; you are saying it can be either, depending on whether the index is "up" or "down"? If you're talking about the canonical momentum which is conjugate to position in the Lagrangian or Hamiltonian pictures, and whose spatial components (i) act as the infinitesimal generators of spatial translations, and (ii) are conserved in the presence of spatial translation symmetry, then that object is a covector. Why does my oak tree have clumps of leaves in the winter? m1=m2. Okay, that's fine. If you're talking about the mass times the 4-velocity, that is a 4-vector. Remember that vectors, like the two-dimensional ones on the right, can be moved around at will without loss of meaning, and that we add them head-to-tail, as shown here. A scalar multiplied by a vector is a vector. The whole "derivation" consists of one trivial step. But again, the metric provides us with an isomorphism, so solving, $$\frac{d}{dt}p_\mu = f_\mu$$ Linear momentum of a system is constant provided there are not external forces acting on any part of the system. Recent Posts. The momentum p of an object of mass m moving with a velocity v is defined as the product of the mass m and the velocity v of the object. I typically write momentum covariantly. For a particle with mass, the momentum equals mass times velocity, and velocity is a vector quantity while mass is a scalar quantity. Assume that the cars stick together following the collision. so as you say, from this perspective force is naturally a one-form. But I don't have an ontological argument to consider that to be an inherent property of momentum. You're talking about $p^\mu = m \dot x^\mu$. Explain the difference between a longitudinal and transverse wave. The variable used to represent momentum is p. The equation to calculate momentum is shown below. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. What's the power loss to a squeaky chain? When our Lagrangian does not depend on (i.e. Bertschinger:Vectors versus one-forms with a metric present: “We should not think of these as being distinct 'components' of the same entity at all.”. Is Momentum A Vector Quantity Or A Scalar Quantity Quora. Without a metric (or some other structure which provides a similar isomorphism), you can't "express it covariantly." @J.Murray If we consider the mythical classical point mass, it has a 4-momentum determined by its mass and its world-line. When passwords of a website leak, are all leaked passwords equally easy to read? Question 5 10 / 10 pts If you know the weight density of a material, which of the following quantities do you need to know to determine the weight of the object? Momentum is frequently expressed as ##p=mv##, where ##p## is momentum, ##m## is mass, and ##v## is the velocity. That means that momentum is a quantity that has a magnitude (or size) and a direction. Momentum has both magnitude and direction. Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. rev 2020.12.10.38158, The best answers are voted up and rise to the top, Physics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us, $p_\mu = \frac{\partial L}{\partial \dot x^\mu}$, $$L(x, \dot x) = m\sqrt{g_{\mu\nu} \dot x^\mu \dot x^\nu}$$, $$\frac{d}{d\tau} p_\mu = -\frac{\partial U}{\partial x^\mu} \equiv f_\mu$$, $$\frac{d}{d\tau} \tilde{p}^\mu =g^{\mu\nu} f_\nu \equiv \tilde{f}^\mu$$. Whether we express it covariantly or contravariantly, the expression refers to the same physical entity. Momentum is a vector quantity. When the can is inverted in the cold water, the can collapses. and If we should not consider a vector and its "canonically" dual 1-form to represent the same object, then it seems that we should be able to say whether 4-momentum, for example, is a vector or a 1-form. Taking the standard Lagrangian. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. To me, the most natural definition of momentum is via the Lagrangian formalism, which yields the one-form $p_\mu = \frac{\partial L}{\partial \dot x^\mu}$. $$\frac{d}{d\tau} \tilde{p}^\mu =g^{\mu\nu} f_\nu \equiv \tilde{f}^\mu$$. What's your trick to play the exact amount of repeated notes. Momenta met in traditional problems often feel just like numbers on a number-line, because only one dimension is considered in order to simplify the problem. A vector quantity possesses both a magnitude and direction. A car accelerates in 12s from 10m/s to 50m/s. Can warmongers be highly empathic and compassionated? I call such a thing a "priority" object. To fully describe the momentum of a 5-kg bowling ball moving westward at 2 m/s, you must include information … DOWNLOAD IMAGE. Diagram Of The Momentum Vectors In The Reaction Plane Of The. Q: The ideal column is subjected to the force F at its midpoint and the axial load P. Determine the max... A: Draw a diagram to show the reactions at the supports. What is the origin of a common Christmas tree quotation concerning an old Babylonish fable about an evergreen tree? How momentum is dual to the velocity vector at a point on a differentiable manifold? This means that the momentum has a direction and that direction is always the same direction as the velocity of an object's motion. Momentum of an object is the product of its mass and velocity (p=m x v). Is partial derivative a vector or dual vector? DOWNLOAD IMAGE. Is a password-protected stolen laptop safe? Momentum is naturally dual to velocity since it usually makes sense to perform the matrix multiplication between momentum (as row vector) and velocity (as column vector) and gets a scalar with units of energy. Yes - Momentum is a vector quantity. Linear Momentum () of a body is defined as the product of the body’s mass and velocity. Have a Free Meeting with one of our hand picked tutors from the UK’s top universities. A scalar quantity possesses only a magnitude and no direction. Impulse Vector Form Examsolutions Maths Tutorials Youtube. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Mass of a body is a scalar quantity but velocity is a vector quantity. From the Lagrangian standpoint, if we add a potential energy term then the Lagrangian equations of motion take the form, $$\frac{d}{d\tau} p_\mu = -\frac{\partial U}{\partial x^\mu} \equiv f_\mu$$ If I want to use the kinds of monsters that appear in tabletop RPGs for commercial use in writing, how can I tell what is public-domain? Use ideas about particles and pressure to explain why the can collapses. A covector maps vector to a scalar. Back when we first discussed momentum, the form of the relativistic momentum was just given and shown to work. However, it is not $p^k = m \dot x^k,\ k=1,2,3$ which is conserved, but rather $p_k = -a^2(t)m\dot x^k$. *Response times vary by subject and question complexity. For a particle with mass, the momentum equals mass times velocity, and velocity is a vector quantity while … It is possible for momentum to change such that the momentum of an object increases, decreases or reverses direction. We need to satisfy these conditions for a quantity to be vector. (where differentiation is taken with respect to the proper time), it then follows that $p_\mu = g_{\mu\nu} m\dot x^\nu$. 2010s TV series about a cult of immortals. A moving body would be a particle with a mass. has a spatial symmetry), as in the case of the free particle motion , the (generalized) momentum is given as , and the Euler-Lagrange equation shows that this quantity is preserved. So if a vector and its dual 1-form are not to be viewed as different representations of the same object, momentum must be one or the other. Momentum is defined as product of mass and velocity of a body. To learn more, see our tips on writing great answers. Either that, or we have … Could any computers use 16k or 64k RAM chips? But, we can also think of momentum as the product of mass with 4-velocity, which is a 4-vector. 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