File Name: conservation of linear and angular momentum .zip
Angular Momentum of a Particle
So far, we have looked at the angular momentum of systems consisting of point particles and rigid bodies. We have also analyzed the torques involved, using the expression that relates the external net torque to the change in angular momentum, Equation In this case, Equation The angular momentum of a system of particles around a point in a fixed inertial reference frame is conserved if there is no net external torque around that point:.
Any of the individual angular momenta can change as long as their sum remains constant. This law is analogous to linear momentum being conserved when the external force on a system is zero.
As an example of conservation of angular momentum, Figure The net torque on her is very close to zero because there is relatively little friction between her skates and the ice. Also, the friction is exerted very close to the pivot point. Consequently, she can spin for quite some time. She can also increase her rate of spin by pulling her arms and legs in. Why does pulling her arms and legs in increase her rate of spin?
The answer is that her angular momentum is constant, so that. It is interesting to see how the rotational kinetic energy of the skater changes when she pulls her arms in.
Her initial rotational energy is. The source of this additional rotational kinetic energy is the work required to pull her arms inward. This work causes an increase in the rotational kinetic energy, while her angular momentum remains constant. Since she is in a frictionless environment, no energy escapes the system. Thus, if she were to extend her arms to their original positions, she would rotate at her original angular velocity and her kinetic energy would return to its original value.
The solar system is another example of how conservation of angular momentum works in our universe. Our solar system was born from a huge cloud of gas and dust that initially had rotational energy. Gravitational forces caused the cloud to contract, and the rotation rate increased as a result of conservation of angular momentum Figure We continue our discussion with an example that has applications to engineering.
Before contact, only one flywheel is rotating. Therefore, the ratio of the final kinetic energy to the initial kinetic energy is. A merry-go-round at a playground is rotating at 4. What is the new rotation rate? The moment of inertia of the system with the bullet embedded in the disk is. As an Amazon Associate we earn from qualifying purchases.
Want to cite, share, or modify this book? This book is Creative Commons Attribution License 4. Skip to Content. University Physics Volume 1 My highlights. Table of contents. Chapter Review. Waves and Acoustics. Answer Key. By the end of this section, you will be able to: Apply conservation of angular momentum to determine the angular velocity of a rotating system in which the moment of inertia is changing Explain how the rotational kinetic energy changes when a system undergoes changes in both moment of inertia and angular velocity.
Figure Her angular momentum is conserved because the net torque on her is negligibly small. The work she does to pull in her arms results in an increase in rotational kinetic energy. The orbital motions and spins of the planets are in the same direction as the original spin and conserve the angular momentum of the parent cloud. A second flywheel, which is at rest and has a moment of inertia three times that of the rotating flywheel, is dropped onto it Figure Because friction exists between the surfaces, the flywheels very quickly reach the same rotational velocity, after which they spin together.
Dismount from a High Bar An He starts the dismount at full extension, then tucks to complete a number of revolutions before landing. His moment of inertia when fully extended can be approximated as a rod of length 1.
If his rotation rate at full extension is 1. See Figure The cylinder is free to rotate around its axis and is initially at rest Figure What is the angular velocity of the disk immediately after the bullet is embedded?
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Authors: William Moebs, Samuel J.
Impulse and Momentum
So far, we have looked at the angular momentum of systems consisting of point particles and rigid bodies. We have also analyzed the torques involved, using the expression that relates the external net torque to the change in angular momentum, Equation In this case, Equation The angular momentum of a system of particles around a point in a fixed inertial reference frame is conserved if there is no net external torque around that point:. Any of the individual angular momenta can change as long as their sum remains constant. This law is analogous to linear momentum being conserved when the external force on a system is zero. As an example of conservation of angular momentum, Figure
Why does Earth keep on spinning? What started it spinning to begin with? And how does an ice skater manage to spin faster and faster simply by pulling her arms in? Why does she not have to exert a torque to spin faster? Questions like these have answers based in angular momentum, the rotational analog to linear momentum. By now the pattern is clear—every rotational phenomenon has a direct translational analog.
Impulse and Momentum
The law of conservation of angular momentum states that when no external torque acts on an object, no change of angular momentum will occur. These examples have the hallmarks of a conservation law. Following are further observations to consider:.
The angular momentum of a particle about a point O is conserved if net torque on the particle about this point is zero i. The angular momentum of a system of particles about a point O is conserved if external torque on the system about this point is zero. A particle undergoes uniform circular motion. About which point on the plane of the circle, will the angular momentum of the particle remain conserved? Solution: In uniform circular motion, the force on the particle passes through centre of the circle so its torque about this point is zero and angular momentum remains conserved.