Finding the force on a shaft when given Watts - shaft design

[cardriverx]

Homework Statement

I think I did this right, but for some reason I am second guessing myself. I don't need help with the whole question, just this part:

The question says "In this exercise, you will design and analyze a shaft and the bearings for use in a power transmission mechanism. You are to produce a detailed drawing of the shaft, including all features necessary to retain the shaft in the bearings and attach the gear. Include all tolerances and dimensions required to manufacture the shaft.

The gear has a 150 mm pitch diameter, and the shaft transmits 1500 W at a speed of 300 rpm."

There is a gear at one end of the shaft, then two bearings, then an end point where it is attached to some component not specified.

So I want to find the force in torque acting on the shaft so that I can actually design it.

Homework Equations

1 W = 1 (N*m)/s

The Attempt at a Solution

300rpm = 5hz (1/s)

5 hz * X N*m= 1500 W

Solve for X, it equals 300 N*m

So then since the radius of the gear is .075m,

300/.075 = 4000N
Is that a valid way to go from Watts when given RPM to force?

Thanks!

 

[cardriverx]

I think I found my error, I need to use rad/s not hz.

so 300 rpm = 31.42 rad/s

31.42*X=1500W

X = 47.7 N*m

But I thought hz is 1/s so when you multiply it by watts it would cancel out the seconds and give you N*m, why does this not work?

 

[Pkruse]

I worked it using a different approach, and got the same answer. I can't see anything wrong with your work.