Name: momentum and impulse diagrams for a particle
Uploaded: 2025-05-22T09:06:16.000Z
Duration: 1 min 20 s
Channel: JoVE

K12 Standards

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South Carolina College and Career Ready Science Standards

High School

Physics

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Motion and Stability: Forces and Interactions

P-PS2-3

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Principle of Linear Impulse and Momentum for a Single Particle

Linear momentum is a vector that shares the same direction as the velocity, while linear impulse measures the effect of a force during the time it acts on the particle.
Consider the equation of motion for a particle of mass m, where acceleration and velocity are measured from an inertial frame of reference.
By integrating the equation with respect to time and rearranging the terms, an equation is obtained which represents the principle of linear impulse and momentum.
It states that the initial momentum of the particle, added to the sum of all the impulses applied to the particle during a specific time period, equals the final momentum of the particle.
These terms can be illustrated using impulse and momentum diagrams.
The momentum diagrams depict the direction and magnitude of the initial and final momentum of the particle, while the impulse diagram represents all the impulses acting on the particle at intermediate points along its path.
The principle can be expressed as three scalar equations by resolving each vector into its components.&#160;

principle of linear impulse and momentum for a single particle

Linear momentum is a fundamental concept in physics that describes the motion of an object. It is a vector quantity, having a magnitude equal to the product of its mass and its velocity, and direction along the object&#39;s velocity. On the other hand, linear impulse, also known as momentum impulse, is a concept in physics related to the change in the linear momentum of an object. Impulse is a vector quantity defined as the product of force and the time over which the force is applied.
Delving into the equation of motion for a particle of mass &#39;m&#39; in an inertial frame, acceleration and velocity are quantified. Integrating this equation over time and rearranging terms yields a formula embodying the principle of linear impulse and momentum. This principle asserts that the sum of the initial momentum of the particle and all applied impulses within a specific timeframe equates to the final momentum. Visualization is facilitated through impulse and momentum diagrams. Momentum diagrams portray the direction and magnitude of initial and final momentum, while the impulse diagram delineates impulses at various points along the particle&#39;s path.
To further elucidate, this principle can be translated into three scalar equations by resolving vectors into components. This analytical approach captures the essence of particle dynamics and establishes a foundation for comprehending real-world scenarios involving motion and force interactions.

Linear momentum is a fundamental concept in physics that describes the motion of an object. It is a vector quantity, having a magnitude equal to the ...

Education

JoVE Core

Mechanical Engineering

Unit 1

Kinetics of a Particle: Impulse and Momentum

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KEY TERMS AND CONCEPTS

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 over time. Rearranging the result gives the principle of linear impulse and momentum. This principle states that the particle’s initial momentum plus all applied impulses over a chosen time period equals its final momentum.

Impulse and momentum diagrams help show this idea clearly. Momentum diagrams show the direction and size of the initial and final momentum. The impulse diagram shows the impulses acting at different points along the particle’s path.

The vector form can also be written as three scalar equations by resolving the vectors into components. This component form is useful for analyzing particle motion in real situations where force and momentum changes must be tracked step by step.

Momentum and Impulse Diagrams for a 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

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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...

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impact: problem solving

Mars Projectile Rebound Height Calculation

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angular momentum

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...

relation between moment of a force and angular momentum

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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 linear momentum, impulse, and impulse-momentum diagrams describe particle motion. See how force over time changes momentum in component form.

Momentum and Impulse Diagrams for a Particle | JoVE K12

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Momentum and Impulse Diagrams for a Particle

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