Name: angular impulse and final velocity
Uploaded: 2025-05-22T09:06:17.000Z
Duration: 1 min 19 s
Channel: JoVE

K12 Standards

Florida Department of Education

High School

Physical Science

SC.912.P.12

SC.912.P.12.6

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

Principle of Angular Impulse and Momentum: Problem Solving

A heavy ball with a known mass is attached to a rod of known length and negligible mass. The system is subjected to a particular torque. Knowing the torque expression and the initial velocity, determine the speed of the ball when t equals 2 seconds.
Initially, a free-body diagram of the system is drawn, and to solve, the angular impulse and momentum principle is recalled.
The principle states that the initial angular momentum of the particle, added to the sum of all the angular impulses applied to the particle during a specific period, equals the final angular momentum of the particle.
The initial and final momenta are calculated as the product of the ball&#39;s mass, the moment arm, and the initial and final velocities, respectively.
While the angular impulse is the integral of the torque over time, the integration is solved by substituting the limits.
By substituting the known quantities into the initial and final momentum equations and rearranging them, the velocity of the ball can be calculated.

principle of angular impulse and momentum: problem solving

Consider a ball of mass m, attached to a massless rod of known length, subjected to a time-dependent torque. If the initial velocity of the mass is known, then the final velocity of the mass for time t can be determined using the principle of angular impulse and momentum.
Initially, a free-body diagram of the system is drawn to illustrate all the forces acting upon the system, providing a crucial understanding of the dynamics at play. Then, the principle of angular impulse and momentum is applied to the system. This principle dictates that the initial angular momentum of an object, added to the sum of all angular impulses exerted on it over a specific period, equates to its final angular momentum.
As a result, the initial and final angular momenta of the sphere are determined by multiplying the sphere&#39;s mass, the moment arm (the perpendicular distance from the axis of rotation to the line of action of the force), and the initial and final velocities, respectively.
Next, the angular impulse is calculated by taking the integral of the torque over the given time interval. The integral can be solved by substituting the limits of the time interval into the equation. Finally, all necessary values are substituted into the initial and final angular momenta equations. By rearranging these equations, the final velocity of the sphere can be calculated.

Consider a ball of mass m, attached to a massless rod of known length, subjected to a time-dependent torque. If the initial velocity of the mass is known, ...

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 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 applied. This principle says that the initial angular momentum plus the angular impulse over a given time equals the final angular momentum. For the sphere, angular momentum is found by using the mass, the moment arm, and the velocity at the start and at the end.

The angular impulse is then found by integrating torque over the time interval. The limits of the interval are substituted into the integral to solve it. After that, the known values are placed into the angular momentum equations, and the equations are rearranged to calculate the final velocity of the sphere.

Angular Impulse and Final Velocity

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

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

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...

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 impulse and momentum connect torque, angular momentum, and velocity. Students solve for a ball’s final speed using a free-body diagram.

Angular Impulse and Final Velocity | 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

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South Carolina College and Career Ready Science Standards

Physics

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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 Impulse and Final Velocity

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