Question

In the equation, Power equals Torque times angular velocity, determine a unit conversion factor such that when the torque is in foot-pounds, the angular velocity is in revolutions per minute the power will be in horsepower. P= ______ x torque x angular velocity. Show your work.

Answer 1

We Know that
1 horse power (hp) = 735.499 Watts
1 W = (1/735.499)hp

Now we know that
1 foot pound = 1.36 Nm
1 revolution per minute = (2/60) rad/s
Hence now
Power = torque (foot-pound)*angular velocity (revolution per minute)
Now convert them by using above conversion , then we get power in watts
Power(watts) = 1.36*torque(foot-pound)*( (2/60)*Angular velocity*(rpm)
Power (W) = 1.36*( (2/60)*Torque*Angular velocity
Now using the watt to hp conversion
Power(1/735.499) hp = 1.36*( (2/60)*Torque*Angular velocity
Power(hp) = 735.499*1.36*( (2/60)*Torque*Angular velocity
Power (hp)= 104.75*Torque*Angular velocity