Flywheel with kinetic friction

[JJBladester]

Homework Statement

It is known that 1500 revolutions are required for the 6000-lb flywheel to coast to rest from an angular velocity of 3000 rpm. Knowing that the radius of gyration of the flywheel is 36 in., determine the average magnitude of the couple due to kinetic friction in the bearings.

Answer:

$$\left |M \right |=87.8lb\cdot ft$$

Homework Equations

$$KE_1+Work=KE_2$$

$$Work_{1\rightarrow 2}=M\theta$$

The Attempt at a Solution

It takes 1500 revolutions to come to rest and 1 revolution = 2$\pi$, so 1500 revolutions = 3000$\pi$.

$$W = 600lbs$$

$$m=\frac{W}{g}=\frac{6000}{9.81}=612lbs$$

$$\omega _1=300\frac{rev}{min}*\frac{2\pi}{1rev}*\frac{1min}{60sec}=10\pi\frac{rad}{sec}$$

Radius of gyration (k) = 36 in = 3 ft

$$KE_1=\frac{1}{2}\bar{I}\omega_1^{2}=\frac{1}{2}\left (k^2m \right )\omega_1^{2}=\frac{1}{2}\left (3^2*612 \right )\left (10\pi \right )^{2}=2.72e^6J$$

$$Work_{1\rightarrow 2}=M\theta=M(3000\pi)$$

$$KE_1+Work=0$$

$$2.72e^6=\left (-3000\pi \right )M$$

$$M=-288.6lb\cdot ft$$

I'm off... but where?

 

[PhanthomJay]

When using weight in pounds, you must divide by g in units of ft/sec^2 in order to get the mass in slugs

 

[JJBladester]

When using weight in pounds, you must divide by g in units of ft/sec^2 in order to get the mass in slugs

It's also customary to write lbf for weight and lb for mass (slugs). Aside from units do you see where my method is incorrect? Thanks in advance Phantom. Happy Thanksgiving.

 

[PhanthomJay]

It's also customary to write lbf for weight and lb for mass (slugs). Aside from units do you see where my method is incorrect? Thanks in advance Phantom. Happy Thanksgiving.

Thank you, same to you.

Your method is fine, but when using the Imperial System of measure, always always always, in Physics, express force units in pounds and mass units in slugs. 1 slug weighs 32.2 pounds on Planet Earth (W = mg), and a force of 1 pound will give amass of 1 slug an acceleration of 1 m/s^2. Any other system of units, if youare not using SI, will lead you astray, guaranteed.

 

[JJBladester]

32.2 pounds

... Yeaaaaa, I used 9.81. Now the math works out. As a certain TV character would say, "DOH!"