The rate at which work is done on a particular axle is measured by the product where T is the torque or turning moment exerted on the axle by the motor or mechanism applied to it for this purpose, and is the angular velocity of the axle in radians per second.
Diameter, w = 44/2 = 22 radians per second, and therefore T= 440,000/22=20,000 lb ft.
If the speed is given in miles per hour, S say, V =1.466 S (6) The revolutions of the axle per second, n, are connected with the radians turned through per second by the relation n =w/27r = w/6.38 (7) § 2.
The general theory of this kind of brake is as follows: - Let F be the whole frictional resistance, r the common radius of the rubbing surfaces, W the force which holds the brake from turning and whose line of action is at a perpendicular distance R from the axis of the shaft, N the revolutions of the shaft per minute, co its angular velocity in radians per second; then, assuming that the adjustments are made so that the engine runs steadily at a uniform speed, and that the brake is held still, clear of the stops and without oscillation, by W, the torque T exerted by the engine is equal to the frictional torque Fr acting at the brake surfaces, and this is measured by the statical moment of the weight W about the axis of revolution; that is T =Fr=WR...
The ratio p is given by e"` e, where e= 2.718; µ is the coefficient of friction and 0 the angle, measured in radians,, subtended by the arc of contact between the rope and the wheel.
For some purposes it is preferable to retain the circular measure, i radians, as being undistinguishable from sin i and tan i when i is small as in direct fire.
Di g d tan i g dt - v cos i ' and now (53) dx d 2 y dy d2xdx Cif dt 2 dt dt2 _ - _ gdt' and this, in conjunction with (46) dy _ d y tan i = dx dt/dt' (47)di d 2 d d 2 x dx sec 2 idt = (ctt d t - at dt2) I (dt), reduces to (48) Integrating from any initial pseudo-velocity U, (60) du t _ C U uf(u) x= C cos n f u (u) y=C sin n ff (a); and supposing the inclination i to change from 0, to 8 radians over the arc.
The ~ force required to constrain the weight a to move in a circle, that is the de viating force, produces an equal and -~ opposite reaction on the shaft, whose X amount F is equal to the centrifugal force Wa2 rig Ib, where r is the radius of the mass centre of the weight, and - a is its angular velocity in radians per second.