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3: Systems of Particles

Last updated

Aug 8, 2022
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- 2.21: Tetrahedra
- 3.1: Introduction to Systems of Particles

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3.1: Introduction to Systems of Particles
In a system of particles, there may be very little or no interaction between the particles (as in a loose association of stars separated from each other by large distances) or there may be (as in the brick) strong forces between the particles. Most (perhaps all) of the results to be derived in this chapter for a system of particles apply equally to an apparently solid body such as a brick.
3.2: Moment of Force
3.3: Moment of Momentum
Moment of momentum plays a role in rotational motion analogous to the role played by linear momentum in linear motion, and is also called angular momentum. Several choices for expressing angular momentum in SI units are possible; the usual choice is J s (joule seconds).
3.4: Notation
In this section I am going to suppose that we n particles scattered through three-dimensional space. We shall be deriving some general properties and theorems – and, to the extent that a solid body can be considered to be made up of a system of particles, these properties and theorems will apply equally to a solid body.
3.5: Linear Momentum
The total momentum of a system of particles equals the total mass times the velocity of the centre of mass.
3.6: Force and Rate of Change of Momentum
3.7: Angular Momentum
3.8: Torque
3.9: Comparison
3.10: Kinetic energy
We remind ourselves that we are discussing particles, and that all kinetic energy is translational kinetic energy.
3.11: Torque and Rate of Change of Angular Momentum
The rate of change of the total angular momentum of a system of particles is equal to the sum of the external torques on the system. The rate of change of the total angular momentum of a system of particles is equal to the sum of the external torques on the system.
3.12: Torque, Angular Momentum and a Moving Point
3.13: The Virial Theorem
The virial Equation tells us whether the cluster is going to disperse or collapse.

Thumbnail: A hoop of radius a rolling along the ground. (Tatum).

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