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.