INTRODUCTION. Xxi 



and r its distance from the axis. The dimension formula for the sum is clearly 

 the same as for each element, and hence is ML'^. The conversion factor is there- 

 fore mf. 



i6. Angular Momentum. — The angular momentum of a body round any 

 axis is the product of the numbers expressing the moment of inertia and the 

 angular velocity of the body. The dimensional formula and the conversion fac- 

 tor are therefore the same as for moment of momentum given above. 



17. Force. — A force is measured by the rate of change of momentum it is 

 capable of producing. The dimension formulas for force and " time rate of 

 change of momentum " are therefore the same, and are expressed by the ratio 



■ of momentum-number to time-number or MLT~^. The conversion factor is thus 

 mlt~'-. 



Note. — When mass is expressed in pounds, length in feet, and time in seconds, the unit force 

 is called the poundal. When grammes, centimetres, and seconds are the corresponding units the 

 unit of force is called the dyne. 



Example. Find the number of dynes in 25 poundals. 



Here m = 453-59' ^ = 30-48, and /= i ; .'. m/r^= 4^3-59 X 30.48= 13825 

 nearly. The number of dynes is thus 13825 X 25 = 345625 approximately. 



18. Moment of a Couple, Torque, or Twisting Motive. — These are dif- 

 ferent names for a quantity which can be expressed as the product of two numbers 

 representing a force and a length. The dimension formula is therefore FL or 

 ML^T~^, and the conversion factor is mlH~'^, 



19. Intensity of a Stress. — The intensity of a stress is the ratio of the num- 

 ber expressing the total stress to the number expressing the area over which the 

 stress is distributed. The dimensional formula is thus FL~- or ML~^T~-, and the 

 conversion factor is nil~'^t~^. 



20. Intensity of Attraction, or " Force at a Point." — This is the force of 

 attraction per unit mass on a body placed at the point, and the dimensional for- 

 mula is therefore FM"^ or LT"'^, the same as acceleration. The conversion fac- 

 tors for acceleration therefore apply. 



21. Absolute Force of a Centre of Attraction, or " Strength of a Cen- 

 tre." — This is the intensity of force at unit distance from the centre, and is there- 

 fore the force per unit mass at any point multiplied by the square of the distance 

 from the centre. The dimensional formula thus becomes FL^M~^ or L*T~^. The 

 conversion factor is therefore Pt~'^. 



22. Modulus of Elasticity. — A modulus of elasticity is the ratio of stress 

 intensity to percentage strain. The dimension of percentage strain is a length 

 divided by a length, and is therefore unity. Hence, the dimensional formula of a 

 modulus of elasticity is the same as that of stress intensity, or ML~^T~'^, and the 

 conversion factor is thus also ml'H'"^. 



