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.
See also Conservation laws.
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