The Angular Momentum Principle: Difference between revisions
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== The Main Idea == | == The Main Idea == | ||
The angular momentum of an object is the product of the moment of inertia and the angular velocity and is a vector quantity. Total angular momentum is equal to the translational angular momentum about a location A plus the rotational angular momentum around the object's center of mass. The angular momentum principle says that derivative of total angular momentum is equal to the torque applied to the object. Torque is equal to the force about a particular location A times the vector from location A to point of application of force (this is a vector product and torque is a vector quantity). Applying a torque to the system changes the angular momentum of the system. The change in angular momentum of a particle relative to location A is equal to the net angular impulse (net torque,A times the change in time). The angular momentum principle is similar to the momentum principle and the angular momentum principle can be used to calculate torque. Angular momentum is conserved so if system gains angular momentum, the surroundings lose that amount. If there is no torque (and therefore no force) applied to the system then the angular impulse is zero and initial angular momentum equals final angular momentum. The angular momentum principle allows you to learn information about initial angular momentum, final angular momentum, change in time and/or torque depending on what variables are known. | |||
== A Mathematical Model == | == A Mathematical Model == | ||
Revision as of 17:39, 30 November 2015
claimed by rhollman6
The Main Idea
The angular momentum of an object is the product of the moment of inertia and the angular velocity and is a vector quantity. Total angular momentum is equal to the translational angular momentum about a location A plus the rotational angular momentum around the object's center of mass. The angular momentum principle says that derivative of total angular momentum is equal to the torque applied to the object. Torque is equal to the force about a particular location A times the vector from location A to point of application of force (this is a vector product and torque is a vector quantity). Applying a torque to the system changes the angular momentum of the system. The change in angular momentum of a particle relative to location A is equal to the net angular impulse (net torque,A times the change in time). The angular momentum principle is similar to the momentum principle and the angular momentum principle can be used to calculate torque. Angular momentum is conserved so if system gains angular momentum, the surroundings lose that amount. If there is no torque (and therefore no force) applied to the system then the angular impulse is zero and initial angular momentum equals final angular momentum. The angular momentum principle allows you to learn information about initial angular momentum, final angular momentum, change in time and/or torque depending on what variables are known.
A Mathematical Model
What are the mathematical equations that allow us to model this topic. For example dp⃗ dtsystem=F⃗ net where p is the momentum of the system and F is the net force from the surroundings.
A Computational Model
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