MecMovies 4.0 : M6.18: Motor-driven Shafts

Diagram shows two shafts marked 1 and 2 of length 36 inches and 96 inches respectively. They are connected by two gears at B which has 24 teeth on the shaft 1 and at C which has 72 teeth on the shaft 2. The shaft 1 is connected to a motor at A. The shaft 2 has a gear at D on which a torque T subscript D is applied.

The relationship between the power transmitted by a shaft and the torque in the shaft is given by:

$P = Tω$

where $P =$ power, $T =$ torque, and $ω =$ rotation speed (in radians per second).

The power supplied by the motor is $15 hp$ , and the rotation speed is $1, 800 rpm$ . Therefore, the torque in shaft $(1)$ can be computed as follows:

$T_{1} = \frac{P}{ω} = \frac{(15 hp) (\frac{550 lb - ft / s}{1 hp})}{(\frac{1, 800 rev}{\min}) (\frac{2 π rad}{1 rev}) (\frac{1 \min}{60 s})} = 43, 768 lb - ft$