# 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.

## 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

B) (2i + 4j -2k)*(-5i + 4j +5k)
((4*-2)-(5*4)) - ((-2*5)-(-5*-4))-((2*4)-(4*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.

Last edited:
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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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