Name: angular momentum and direction
Uploaded: 2024-03-07T13:22:21.000Z
Duration: 1 min 21 s
Channel: JoVE

K12 Standards

Florida Department of Education

High School

Physical Science

SC.912.P.12

SC.912.P.12.6

Angular Momentum

Angular momentum describes the rotational motion of an object.
It is defined as the moment of the object&#39;s linear momentum about a specific point O.
Consider a particle following a curved path in an x-y plane.
The scalar formulation determines the magnitude of its angular momentum, where r represents the moment arm or the perpendicular distance from point O to the line of action of the linear momentum.
However, angular momentum is a vector quantity. So, using a right-hand thumb rule the direction of the angular momentum is shown to be perpendicular to the rotation plane.
Now, if a particle follows a space curve, the vector cross-product can help determine the angular momentum around a particular point.
In this vector representation, the angular momentum remains orthogonal to the plane encompassing the position vector and the linear momentum.
When calculating the cross product, the position vector and the linear momentum should be expressed using their Cartesian components. The angular momentum is then determined by evaluating the formed determinant.

angular momentum

Angular momentum characterizes an object&#39;s rotational motion and is defined as the moment of its linear momentum about a specified point O. When a particle moves along a curved path in the x-y plane, the scalar formulation calculates the magnitude of its angular momentum, utilizing the moment arm (d), representing the perpendicular distance from point O to the line of action of the linear momentum. Despite being scalar in formulation, angular momentum is inherently a vector quantity. Its direction is ascertained through the right-hand rule, perpendicular to the rotation plane.
If the particle traces a space curve, the vector cross-product becomes instrumental in determining the angular momentum around a specific point. In this representation, the angular momentum maintains orthogonality to the plane formed by the position vector and linear momentum. For computations involving the cross product, expressing the position vector and linear momentum in Cartesian components is crucial. The angular momentum is then established by evaluating the determinant formed by these components. This comprehensive approach ensures an accurate representation of angular momentum in both magnitude and direction for objects undergoing rotational motion.

Angular momentum describes the rotational motion of an object.
It is defined as the moment of the object&#39;s linear momentum about a specific point O.
...

Education

JoVE Core

Mechanical Engineering

Unit 1

Kinetics of a Particle: Impulse and Momentum

kinetics-of-a-particle-impulse-and-momentum

KEY TERMS AND CONCEPTS

angular momentum and direction

Angular momentum describes rotational motion and the direction of that motion. It is defined as the moment of a particle’s linear momentum about a chosen point O. This makes it useful for describing how motion curves around a point.

For a particle moving along a curved path in the x-y plane, the scalar form gives the magnitude of angular momentum. It uses the moment arm, d, which is the perpendicular distance from point O to the line of action of the linear momentum. Even when written in scalar form, angular momentum is still a vector quantity.

Its direction is found with the right-hand rule. The angular momentum vector points perpendicular to the plane of rotation. When a particle follows a space curve, the vector cross product is used to find angular momentum about the chosen point.

In that case, angular momentum is orthogonal to the plane formed by the position vector and the linear momentum. To calculate it, the position vector and linear momentum are written in Cartesian components. The angular momentum is then found by evaluating the determinant built from those components.

Angular Momentum and Direction

principle of linear impulse and momentum for a single particle

principle-of-linear-impulse-and-momentum-for-a-single-particle

Momentum and Impulse Diagrams for a Particle

Linear momentum describes how a particle moves in physics. It is a vector quantity, so it has both size and direction. Its magnitude equals mass times velocity, and its direction matches the particle’s velocity. Linear impulse, also called momentum impulse, describes the change in linear momentum. It is also a vector quantity. Impulse equals force multiplied by the time interval over which the force acts. For a particle of mass m in an inertial frame, the equation of motion can be integrated...

principle of linear impulse and momentum for a single particle: problem solving

principle-linear-impulse-momentum-for-single-particle-problem

Solving a Two-Mass Pulley Momentum Problem

A massless pulley system with a wooden box and a cylinder shows how linear impulse and momentum can be used to find motion after release. The two objects have known masses, m1 and m2, and the system starts from rest before it is released. The rope length stays constant as the box and cylinder move. That means the rope can be written as a set of smaller segments attached to each object. Taking the time derivative of the full rope length gives the velocity relation between the wooden box and the...

principle of linear impulse and momentum for a system of particles

principle-of-linear-impulse-and-momentum-for-a-system-of-particles

Center of Mass and Particle Momentum

A system of particles follows an equation of motion that describes how external forces affect its motion in an inertial frame of reference. The particles also exert internal forces on one another, but these forces act in equal and opposite collinear pairs. Because they cancel, they do not appear in the equation of motion. The principle of linear impulse and momentum comes from integrating that equation of motion over time. After the limits are applied, the combined initial linear momenta of...

conservation of linear momentum for a system of particles

conservation-of-linear-momentum-for-a-system-of-particles

Momentum Transfer in Billiard Collisions

Momentum transfer in billiard collisions shows how linear momentum changes when one ball strikes another. A moving cue ball hits a stationary ball and gives up part of its linear momentum. The cue ball slows down, and the other ball starts moving. The collision force acts for an extremely short time, so its impulse is negligible. In impulse-momentum analysis, forces are grouped as impulsive or non-impulsive. Impulsive forces act briefly but can cause a large momentum change. For a system of...

impact

Impact, Impulse, and Restitution

Impact describes what happens when two bodies collide and impulsive forces act between them. In impact mechanics, the colliding particles move along the line of impact. This line passes through their centers and is perpendicular to the contact plane. When particles with different initial velocities collide, they apply equal and opposite impulses and cause deformation. At maximum deformation, the particles move together with the same velocity. After that, restitution begins. Restitution is the...

types of impact

Central and Oblique Collision Dynamics

Impact events are described by how two objects collide and how they move after the collision. The two main forms are central impact and oblique impact. A central impact happens when objects strike head-on, with opposite velocities along the line of impact. An oblique impact happens when objects collide at an angle. In this case, both direction and velocity can change after the collision. This makes the motion after impact more complex than in a head-on collision. The coefficient of...

impact: problem solving

Mars Projectile Rebound Height Calculation

Mars projectile rebound height calculation uses kinematics and the coefficient of restitution. A rover launches a projectile, and the projectile hits the Martian surface before bouncing upward again. The goal is to find the maximum height it reaches after the collision. The launch point is taken as the origin. Upward velocity is treated as positive, and the horizontal velocity stays constant. Using the known initial velocity and Mars gravity, the vertical velocity at impact is calculated with...

Angular momentum describes rotational motion and the direction of that motion. It is defined as the moment of a particle’s linear momentum about a chosen point O. This makes it useful for describing how motion curves around a point. For a particle moving along a curved path in the x-y plane, the scalar form gives the magnitude of angular momentum. It uses the moment arm, d, which is the perpendicular distance from point O to the line of action of the linear momentum. Even when written in...

relation between moment of a force and angular momentum

relation-between-moment-of-a-force-and-angular-momentum

Torque and Angular Momentum in Rotation

Torque and angular momentum explain how force changes rotation. When a force acts at a distance from the center, it creates torque. A spinning top is a simple example of this idea. Moment is the rotational form of force. It shows how a force can start rotational motion. Angular momentum is the rotational form of linear momentum. It describes an object’s tendency to keep rotating. The rate of change of angular momentum can be written as a derivative. In that expression, the first term becomes...

principle of angular impulse and momentum

principle-of-angular-impulse-and-momentum

Angular Impulse, Momentum, and Rotation

Angular impulse and momentum describe how forces change an object's rotation over time. The idea connects the moment of force, or torque, with angular momentum. When the equation is integrated from an initial time to a final time, it gives the angular impulse and momentum principle. The principle defines initial and final angular momentum as the moments of a particle's linear momentum at those specific times. Angular impulse is found by integrating the moments of all forces acting on the...

principle of angular impulse and momentum: problem solving

principle-of-angular-impulse-and-momentum-problem-solving

Angular Impulse and Final Velocity

Angular impulse and momentum help determine the final velocity of a ball attached to a massless rod. The ball has mass m and moves under a time-dependent torque. If the initial velocity is known, the final velocity after a time interval can be found with this principle. The first step is to draw a free-body diagram. A free-body diagram shows all the forces acting on the system. It helps make the motion and rotation easier to analyze. Next, the principle of angular impulse and momentum is...

steady flow of a fluid stream

Fluid Force and Momentum in a Pipe

Fluid force and momentum in a pipe are linked through a control volume with solid boundaries. As fluid moves through the pipe, the walls can change its direction by exerting an impulse through the resulting force. This setup helps show how flow behaves inside a fixed region. For steady flow, the mass entering the control volume at time t with velocity v1 equals the mass leaving after a small time dt with velocity v2. Over that same interval, the momentum inside the control volume stays...

key terms and concepts

Learn how angular momentum is measured as a particle’s rotational motion, including scalar magnitude, moment arm, right-hand rule, and cross-product calculation.

Angular Momentum and Direction | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

mechanical engineering

south-carolina-college-and-career-ready-science-standards

South Carolina College and Career Ready Science Standards

Physics

motion-and-stability-forces-and-interactions

Motion and Stability: Forces and Interactions

P-PS2-3

Introduction to Scalars

Many familiar physical quantities can be specified completely by giving a single number and the appropriate unit. For example, &#34;a class period lasts ...

Introduction to Vectors

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Vector Components in the Cartesian Coordinate System

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Vector Algebra: Graphical Method

Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the ...

Vector Algebra: Method of Components

It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like ...

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Scalar Product (Dot Product)

The scalar multiplication of two vectors is known as the scalar or dot product. As the name indicates, the scalar product of two vectors results in a ...

Vector Product (Cross Product)

Vector multiplication of two vectors yields a vector product, with the magnitude equal to the product of the individual vectors multiplied by the sine of ...

Scalar and Vector Triple Products

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In mathematics and physics, the gradient and del operator are fundamental concepts used to describe the behavior of functions and fields in space. The ...

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Divergence and Curl

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Second Derivatives and Laplace Operator

The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or ...

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Line, Surface, and Volume Integrals

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Distinguish between scalar and vector quantities and assess which should be used to describe an event.

SC.912.P.12.1

Position and Displacement

The position of an object defines its location relative to a convenient frame of reference at any particular time. A frame of reference is an arbitrary ...

Average Velocity

To calculate the other physical quantities in kinematics, we must introduce the time variable. The time variable allows us not only to state the position ...

Instantaneous Velocity - I

The average velocity during a time interval cannot tell us how fast or in what direction a particle is moving at any given time during the interval. To ...

Instantaneous Velocity - II

Instantaneous velocity is the quantity that measures how fast an object is moving along its path. In other words, the instantaneous velocity of an object ...

Average Acceleration

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Instantaneous Acceleration

Acceleration is in the direction of the change in velocity, but it is not always in the direction of motion. When an object slows down, its acceleration ...

Kinematic Equations - I

When an object moves with constant acceleration, the velocity of the object changes at a constant rate throughout the motion. The kinematic equations of ...

Kinematic Equations - II

The second kinematic equation expresses the final position of an object in terms of its initial position, the distance traveled with the initial constant ...

Kinematic Equations - III

The first two kinematic equations have time as a variable, but the third kinematic equation is independent of time. This equation expresses final velocity ...

Kinematic Equations: Problem Solving

When analyzing one-dimensional motion with constant acceleration, the problem-solving strategy involves identifying the known quantities and choosing the ...

Free-falling Bodies: Introduction

All objects, neglecting air resistance, fall with the same acceleration towards the Earth&#39;s center due to the force exerted by the Earth&#39;s ...

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Velocity and Position by Graphical Method

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In&#160;uniform circular motion, the particle executing circular motion has a constant speed, and the circle is at a fixed radius. However, not all ...

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If acceleration as a function of time is known, then velocity and position functions can be derived using integral calculus. For constant acceleration, ...

Relative Velocity in One Dimension

The understanding of the concept of reference frames is essential to discuss relative motion in one or more dimensions. When we say that an object has a ...

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Relative Velocity in Two Dimensions

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Average and Instantaneous Velocity Vectors

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Projectile Motion: Equations

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Projectile Motion: Example

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Uniform Circular Motion

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Analyze the motion of an object in terms of its position, velocity, and acceleration (with respect to a frame of reference) as functions of time.

SC.912.P.12.2

Newton's First Law: Introduction

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Newton's First Law: Application

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Internal and External Forces

Newton&#39;s first law states that a net external force causes a change in motion. External forces act on an object or system, originating outside of the ...

Newton's Second Law

Newton&#39;s second law is closely related to his first law of motion. It mathematically gives the cause-and-effect relationship between force and changes ...

Newton's Third Law: Introduction

Whenever one body exerts a force on a second body, the first body experiences a force equal in magnitude and opposite in direction, to the force that it ...

Newton's Third Law: Examples

Newton&#39;s third law states that every action has an equal and opposite reaction. Consider a swimmer pushing off the side of a pool. They push against ...

Inertial Frames of Reference

Newton&#8217;s first law is usually considered to be a statement about reference frames. It provides a method for identifying a special type of reference ...

Non-inertial Frames of Reference

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First Law: Particles in One-dimensional Equilibrium

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first-law-particles-in-two-dimensional-equilibrium

First Law: Particles in Two-dimensional Equilibrium

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Second Law: Motion under Same Force

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Second Law: Motion under Same Acceleration

Newton&#39;s second law of motion applies to bodies moving under the same acceleration. For example, when a baggage tractor pulls luggage carts, each cart ...

Interpret and apply Newton's three laws of motion.

SC.912.P.12.3

Gravitation

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Newton's Law of Gravitation

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Gravitation Between Spherically Symmetric Masses

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Gravity between Spherical Bodies

Newton&#39;s law of gravitation describes the gravitational force between any two point masses. However, for extended spherical objects like the Earth, ...

Describe how the gravitational force between two objects depends on their masses and the distance between them.

SC.912.P.12.4

A. Motion can be measured and described qualitatively and quantitatively. Net forces create a change in motion. When objects travel at speeds comparable to the speed of light, Einstein's special theory of relativity applies.

B. Momentum is conserved under well-defined conditions. A change in momentum occurs when a net force is applied to an object over a time interval.

C. The Law of Universal Gravitation states that gravitational forces act on all objects irrespective of their size and position.

D. Gases consist of great numbers of molecules moving in all directions. The behavior of gases can be modeled by the kinetic molecular theory.

E. Chemical reaction rates change with conditions under which they occur. Chemical equilibrium is a dynamic state in which forward and reverse processes occur at the same rates.

Angular Momentum and Direction

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