INTRODUCTION. XXvii 



Velocity, v, of a body is dL/dt, or the ratio of a length to a time. The dimen- 

 sional formula is [Lr~^3- 



Angle is measured by the ratio of the length of an arc to its radius. The di- 

 mensional formula is unity. 



Angular Velocity is the ratio of the angle described in a given time to that 

 time. The dimensional formula is C^"G- 



Linear Acceleration is the rate of change of velocity or a = dv/dt. The dimen- 

 sional formula is [^FT^^J or [LT^^]. 



Ex. — A body acquires velocity at a uniform rate and at the end of one minute moves at the 

 rate of 20 kilometers per hour: what is the acceleration in centimeters per second per second? 

 Since the velocity gained was 20 km per hour in one minute, the acceleration was 1200 km 

 per hour per hour. / = looooo, / = 3600, //"^ = 100000/3600* = 0.00771; the acceleration = 

 .00771 X 1200 = 9.26 cm/sec. 



Angular Acceleration is rate of change of angular velocity. The dimensional 

 formula is [(angular velocity)/ T] or [T^^]. 



Momentum, the quantity of motion in the Newtonian sense, is measured by 

 the product of the mass and velocity of the body. The dimensional formula is 

 [MF] or IMLT-'J 



Moment of Momentum of a body with reference to a point is the product of 

 its momentum by the distance of its line of motion from the point. The dimen- 

 sional formula is \^MUT~^']- 



Moment of Inertia of a body round an axis is expressed by the formula Swr^, 

 where m is the mass of any particle of the body and r its distance from the axis, 

 The dimensional formula for the sum is the same as for each element and is. 



[ML2]. 



Angular Momentum of a body is the product of its moment of inertia and 

 angular velocity. The dimensional formula is \^ML^T~^2. 



Force is measured by the rate of change of momentum it can produce. The 

 dimensional formulae for force and "time rate of change of momentum" are 

 therefore the same, the ratio of a momentum to a time [^MLT~^']- 



Ex. — When mass is expressed in lbs., length in ft., and time in sees., the unit force is called 

 the poundal. When grams, cms, and sees, are the corresponding units, the unit of force is 

 called the d>'ne. Find the nMmber of dynes in 25 poundals. Here m = 453.59, / = 30.48, / = i; 

 mii'^ = 453.59 X 30.48 = 13825 nearly. The number of dynes is 13825 X 25 = 345625 approxi- 

 mately. 



Moment of Couple, Torque, or Twisting Motive can be expressed as the product 

 of a force and a length. The dimensional formula is [_FL] or [il/L^T^^j 



Intensity of Stress is the ratio of the total stress to the area over which the 

 stress is distributed. The dimensional formula is [_FL~'^'2 or [ML'^T^^J 



Intensity of Attraction, or " Force at a Point," is the force of attraction per 

 unit mass on a body placed at the point. The dimensional formula is [Flf~^3 

 or [Z,r~'^3> the same as acceleration. 



