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2   PRINCIPLES OF ELEMENTARY DYNAMICS

TRANSLATION AND ROTATION   3

ing a constant direction of motion has a constant linear acceleration in the direction of motion of the value

a-v`-v0   (2)

t

A body moving in a circular path of radius r with constant speed v has an acceleration directed toward the center of the circle. The magnitude of this so-called " radial acceleration " or " centripetal acceleration " is

Commonly employed units of linear acceleration are the centimeter per second per second, the foot per second per second, and the mile per hour per second.

Any cause which either produces or tends to produce a linear acceleration of the motion of a body is called force. Commonly employed units of force are the dyne, gram weight, and pound weight.

1 pound weight = 454 grams weight

At a place where the acceleration due to gravity is 980 centimeters per second per second

1 gram weight = 980 dynes

Work is the accomplishment of a change in the position of a body against an opposing force. The magnitude of the work is taken to be equal to the product of the force overcome and the projection of the displacement in the line of action of the force.

W = Fx   (4)

The commonly employed units of work are the erg (dyne-centimeter), joule (10' ergs), and the foot-pound.

Energy is stored work. The amount of energy possessed by a system of bodies is the amount of work it can do in passing from its present condition to some standard condition.

The kinetic energy of translation of a body of mass m moving with a linear speed v is

W, = amv2   (5)

Energy, being work, is measured in the same units as work. Power is the time-rate of doing work. If a system does an amount of work W in time t by opposing a constant force F

through a distance x along the line of action of the force, the power P has the value

P = W = Fx - Fv   (6)

The units of power are the erg per second, the watt (joule per second), the foot-pound per second, and the horse-power (= 550 footpounds per second).

That property of a body which makes it necessary to use force to produce a linear acceleration in the motion of the body is called inertia. Inertia is measured by the tendency of a body to keep its linear velocity of constant magnitude and in an invariable direction. Anything which possesses inertia is called matter. The amount of matter in a body is called the mass of the body. The ratio of the masses of two bodies is taken to be equal to the ratio of the inertias of the bodies. The inertia of a body or system of bodies equals the sum of the masses of its parts. Commonly employed units of mass are the gram, the pound, and the slug or British engineering unit of mass. At a place where the acceleration due to gravity is 32.1 ft. per sec. per sec.,

1 slug = 32.1 lb.

The product of the mass of a body and its linear velocity is called the linear momentum of the body. The units used are the gram-centimeter per second and the slug-foot per second. These units have no name but are referred to as the centimeter-gramsecond absolute unit and the British en

A

gineering unit of linear momentum, re

spectively.

2. Angular Motion: Definitions and C

Units. - Angular displacements are commonly measured in degrees, radians or

revolutions. The degree is one-ninetieth part of a right angle. The radian is the plane angle subtended at the center of a circle by an arc equal to the radius of the circle. Thus, if the arc AB, Fig. 1, is half as long as the radius CA, the angle 0 is one-half of a radian. Whatever the length x of the arc, and the length r of the radius

¢ = r radians   (7) 1 revolution = 27r radians = 360°. 1 radian = 57.3° = 3438'.

a'   V2

r

(3)

r

FIG. 1

B

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