Angular momentum using unit-vector notation

In summary, the conversation is discussing the calculation of angular momentum and torque on a 0.25 kg object with a force of 4.0j N acting on it. The object's position vector is (2.0t - 2.0k) m and velocity vector is (-5.0i + 5.0k) m/s, and the equations for torque and kinetic energy are mentioned. The solution for finding the object's angular momentum requires using a cross product.
  • #1
maxalador
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Homework Statement



At one instant, force F: 4.0j N acts on a 0.25 kg object that has position^vector^V : (2.0t - 2.0k) m and velocity vector /: (-5.0i + 5.0k) m/s. About the origin and in unit- vector notation, what are (a) the object's angular momentum and (b)the torque acting on the object

m = .25kg
f = (4.0 N)j
v = (-5i + 5k)

Homework Equations



Torque = (Yz-Zy)+(Zx-Xz)+(Xy-Yx)
KE= 1/2mv^2 + 1/2lw^2

The Attempt at a Solution



A) not quite sure where to start with A

B) (2i + 4j -2k)*(-5i + 4j +5k)
((4*-2)-(5*4)) - ((-2*5)-(-5*-4))-((2*4)-(4*2))
 
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  • #2
Just remember that angular momentum is given by:$$\stackrel{\rightarrow}{l} = \stackrel{\rightarrow}{r} \times \stackrel{\rightarrow}{p}$$ So finding it just means doing another cross product.
 
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What is angular momentum?

Angular momentum is a physical quantity that describes the rotational motion of an object. It is a vector quantity, meaning it has both magnitude and direction.

How is angular momentum calculated?

Angular momentum is calculated by multiplying the moment of inertia of an object by its angular velocity. It can also be expressed using unit-vector notation, which is a mathematical notation that represents a vector as a combination of its magnitude and direction.

What is unit-vector notation?

Unit-vector notation, also known as component form, is a mathematical notation that represents a vector as a combination of its magnitude and direction using unit vectors. These unit vectors are typically denoted by i, j, and k for the x, y, and z directions respectively.

How is unit-vector notation used in angular momentum calculations?

In angular momentum calculations, unit-vector notation is used to express the angular velocity as a vector in terms of its components along the x, y, and z axes. This allows for a more precise and concise representation of the vector quantity.

What are the advantages of using unit-vector notation for angular momentum?

Using unit-vector notation in angular momentum calculations allows for a more versatile and general representation of the vector quantity. It also simplifies calculations and makes it easier to visualize the direction of the vector in three-dimensional space.

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