# Ballistics

## Projectile Motion With Air Resistance

If projectiles were only launched from the surface of the moon where there is no atmosphere, then the effects of gravity, as described in the previous section, would be sufficient to determine the flight path. On Earth, however, the atmosphere will influence the motion of projectiles. As opposed to the situation due to purely gravitational effects, projectile motion with air resistance will be dependent on the weight and shape of the object. As one would suspect, lighter objects are more strongly affected by air resistance. In many cases, air resistance will produce a drag force which is proportional to the velocity squared. The effects of increased air drag on an object such as a cannon ball will cause it to fall short of its normal range without air resistance. This effect may be significant. In World War I, it was realized that cannon balls would travel farther distances if aimed at higher elevations, due to the decreased air density and decreased drag.

More subtle effects of air resistance on projectile motion are related to the shape and rotation of the object. Clearly, the shape of an object can have an effect on its projectile motion, as anyone has experienced by wadding up a piece of paper before tossing it into the waste can. The rotation of an object is important also. For example, a good quarterback always puts a spin on a football when making a pass. By contrast, to produce an erratic flight, a knuckle ball pitcher in baseball puts little or no spin on the ball. The physical property that tends to keep spinning objects spinning is the conservation of angular momentum. Not only do spinning objects tend to keep spinning but the orientation of the spin axis tends to remain constant. This property is utilized in the design of rifle barrels that have spiral grooves to put a spin on the bullet. The spinning of the bullet around its long axis will keep the bullet from tumbling and will increase the accuracy of the rifle. This property is also utilized in designing guidance systems for missiles. These guidance systems consist of a small spinning device called a gyroscope, which keeps a constant axis orientation and thus helps to orient the missile. Small deviations of the missile with respect to the orientation of the gyroscope can be measured and corrections in the flight path can be made.

## Resources

### Books

Armenti, Angelo Jr. The Physics of Sports. New York: American Institute of Physics, 1992.

Hewitt, Paul. Conceptual Physics. Englewood Cliffs, NJ: Prentice Hall, 2001.

Munson, Bruce, et al. Fundamentals of Mechanics. 4th ed. New York: John Wiley and Sons, 2002.

Kurt Vandervoort

## KEY TERMS

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Acceleration of gravity

—The vertical downward acceleration equal to 32 ft (9.8 m) per second per second experienced by objects in flight close to Earth.

Air resistance

—The drag force on an object in flight due to the interaction with air molecules.

Free falling body

—A falling object in one dimensional motion, influenced by gravity when air resistance is negligible.

Gyroscope

—A device similar to a top, which maintains rotation about an axis while maintaining a constant orientation of that axis in space.

Inertia

—The tendency of an object in motion to remain in motion in a constant direction and at a constant speed, and the tendency of an object at rest to remain at rest.

Projectile

—An object that is projected close to Earth and whose flight path is determined by gravity, air resistance, and inertia.