2010s TV series about a cult of immortals. The length, or magnitude, of a momentum vector is how much momentum there is, and its direction is the direction of the momentum, or its velocity component. Okay, that's fine. Vector Quantity and Momentum: Vector quantities are those quantities which have a magnitude as well as a direction. When the can is inverted in the cold water, the can collapses. The variable used to represent momentum is p. The equation to calculate momentum is shown below. *Response times vary by subject and question complexity. It only takes a minute to sign up. How long does it take to deflate a tube for a 26" bike tire? 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. For a particle with mass, the momentum equals mass times velocity, and velocity is a vector quantity while … 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. 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, $p_\mu = \frac{\partial L}{\partial \dot x^\mu}$, $$L(x, \dot x) = m\sqrt{g_{\mu\nu} \dot x^\mu \dot x^\nu}$$, $$\frac{d}{d\tau} p_\mu = -\frac{\partial U}{\partial x^\mu} \equiv f_\mu$$, $$\frac{d}{d\tau} \tilde{p}^\mu =g^{\mu\nu} f_\nu \equiv \tilde{f}^\mu$$. m1=m2. Asking for help, clarification, or responding to other answers. Why does my oak tree have clumps of leaves in the winter? The whole "derivation" consists of one trivial step. Are contravariant basis vectors and basis 1-forms identical? The momentum you referred to before is well-defined on its own, but you can't map it to a covector without implicitly making a choice of metric (or other index-lowering map). In this case, the surface has a null tangent $\ell^{a}$ and a null normal vector $k^{a}$, and it will work out that the covariant three space is spanned by the two metric plus $\ell^{a}$, but the correct oneform to use to span the covariant space is $k_{a}$ plus the spanning oneforms on the two-space. https://physics.stackexchange.com/a/576885/117014, infinitesimal generators of spatial translations. Simple explanation of why momentum is a covector? If we picture a car driving down the road with momentum p: the momentum of the car has both magnitude and direction (the direction of this momentum is the direction in which the car is traveling). 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. @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 being the product of a scalar quantity and a vector quantity, it is also a vector quantity. A scalar multiplied by a vector is a vector. Mass is a scalar; it doesn’t have any direction associated with it, only its magnitude. 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. That being said, this is clearly the brother of the 4-vector $\tilde{p}^\mu = m \dot x^\mu$, with the index raised/lowered via the metric. DOWNLOAD IMAGE. It collides with a car (m2) traveling east at 22 m/s. To fully describe the momentum of a 5-kg bowling ball moving westward at 2 m/s, you must include information … Yes - Momentum is a vector quantity. That means that momentum is a quantity that has a magnitude (or size) and a direction. mass Correct! 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. Impulse is the change of momentum. What's the power loss to a squeaky chain? This expression is perfectly well-defined with no additional structure needed. 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. whereas velocity is a vector quantity. We can also see that momentum is a vector quantity as a vector quantity is one that has both magnitude and direction. Making statements based on opinion; back them up with references or personal experience. Momentum is a derived quantity, calculated by multiplying the mass, m (a scalar quantity), times velocity, v (a vector quantity). MathJax reference. I could ask the same thing about the electromagnetic field tensor, but momentum seems to be a good place to start. Momentum is frequently expressed as ##p=mv##, where ##p## is momentum, ##m## is mass, and ##v## is the velocity. This metric is homogeneous and isotropic, which implies 3-momentum conservation. In what countries/programs is a graduate student bonus common? When passwords of a website leak, are all leaked passwords equally easy to read? Momentum is defined as product of mass and velocity of a body. 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? The SI … Without a metric (or some other structure which provides a similar isomorphism), you can't "express it covariantly." Use MathJax to format equations. 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. $$\frac{d}{d\tau} \tilde{p}^\mu =g^{\mu\nu} f_\nu \equiv \tilde{f}^\mu$$. What adjustments do you have to make if partner leads "third highest" instead of "fourth highest" to open? A car accelerates in 12s from 10m/s to 50m/s. Is Momentum A Vector Quantity Or A Scalar Quantity Quora. This is a follow-on to https://physics.stackexchange.com/a/576885/117014. From the Lagrangian standpoint, if we add a potential energy term then the Lagrangian equations of motion take the form, $$\frac{d}{d\tau} p_\mu = -\frac{\partial U}{\partial x^\mu} \equiv f_\mu$$ However, it is not $p^k = m \dot x^k,\ k=1,2,3$ which is conserved, but rather $p_k = -a^2(t)m\dot x^k$. I typically write momentum covariantly. 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. DOWNLOAD IMAGE. As discussed in an earlier unit, a vector quantity is a quantity that is fully described by both magnitude and direction. The Energy-Momentum Vector. Is momentum a vector or a scalar quantity? One Dimension. Impulse Vector Form Examsolutions Maths Tutorials Youtube. ⃗⃗⃗ = m ∙ Momentum is a vector quantity that has the same direction as the velocity of the object and a magnitude m times the velocity. Mass is an example of a scalar quantity (mass doesn't point in any direction!) 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. Linear Momentum () of a body is defined as the product of the body’s mass and velocity. 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 a vector because it is the product of a scalar and a vector. so as you say, from this perspective force is naturally a one-form. As a concrete example, consider the flat space FLRW spacetime in which, $$ds^2= c^2dt^2 - a^2(t)\big(dx^2+dy^2+dz^2\big)$$. @J.Murray If we consider the mythical classical point mass, it has a 4-momentum determined by its mass and its world-line. Construction of the Momentum 4-Vector. 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