8. Impulse and Momentum…………………
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As you gaze up at the stars, you can’t help but wonder about the vast expanse
of space that surrounds this seemingly lonely planet. Is the Earth the only planet that
sustains life, or is there life elsewhere? At the very least, are there planets with water,
air, and ranges of temperature that are fit for human habitation? Most scientists believe
that the likelihood is high that there is a planet other than our own that can sustain life.
If and when such a planet is discovered, will we have the technological skills
to send a ship on a voyage to explore it? For centuries, man has contemplated traveling
to other planets. Our ability to travel to other planets is rooted in engineering principles
– among them the principles of linear momentum and angular momentum.
The linear momentum of a particle is defined as the product of the particle’s
mass and its velocity. The angular momentum of a particle about a given point is
defined as the product of the particles linear momentum and the moment arm between
the given point and the line of action of the particle’s linear momentum. Aerospace
engineers use linear momentum and angular momentum principles in the design of
aerospace vehicles, like rockets, satellites, and interplanetary probes.
It follows from momentum principles that the linear momentum of an
aerospace vehicle can only be changed through the application of external forces.
Likewise, the angular momentum of an aerospace vehicle can only be changed through
the application of external moments. It’s not possible to place a device on an aerospace
vehicle that can change its linear momentum or its angular momentum. The change of
the vehicle’s momentum must be created by external forces and external moments,
rather than be created internally.
One way around the inability to change momentum by external forces and
external moments is to divide the aerospace vehicle into two subsystems, in which the
momentum of one subsystem is controlled at the expense of the other.
In rocketry, the system is divided into propellant and the rest of the vehicle.
The downward flow of the propellant from the rocket creates an upward impulse that
acts on the rest of the rocket to increase its linear momentum. Although the linear
momentum of the total system (propellant plus vehicle) is not being changed by the
internal forces, the downward linear momentum of the propellant is countered by the
upward momentum of the vehicle.
Aerospace engineers control the spin rates in spin-stabilized satellites using a
similar approach. The spin rates are controlled by placing spinning wheels inside the
satellites. The wheels are called momentum wheels. The momentum wheels represent
one subsystem and the rest of the satellite represents the other subsystem. Changing
the angular momentum of the momentum wheels about a given axis creates an angular
impulse on the rest of the satellite, causing its angular momentum to change in the
opposite direction – thereby controlling the spin rates of the satellite. A practical
problem with this solution, however, is that the momentum wheels can build up
angular speed over time and eventually spin at prohibitively high angular rates. The
only way to overcome this problem is through the application of external moments. In
satellites that orbit around the Earth, the external moments can be generated from the
Earth’s magnetic field. A loop of current in an electrical circuit inside the satellite
reacts with the Earth’s magnetic field to create an external moment that acts on the
momentum wheels. Although the external moment is relatively small, it’s big enough
to prevent the angular rates of the momentum wheels from growing. This process of
reducing the angular momentum of momentum wheels is called momentum dumping.
In this chapter you’ll see that momentum principles, like energy principles,
can be used to describe the behavior of engineering systems instead of using Newton’s
Laws directly. Rather than look at the forces acting on objects, it is sometimes more
insightful to look at the object’s linear momentum and angular momentum. As with
energy principles, you’ll see that the use of momentum principles can also save a
considerable amount of time and effort when solving many problems.
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