Rigid Body Rotation Application

[lanew]

Homework Statement

I'm trying to include rigid body rotation in a problem I'm working on but can't seem to figure it out.

Two shafts oriented vertically are connected by a thin cross member of length $R$. Holding one shaft stationary and applying a constant tangential load $F$ to the other shaft will cause rotation at some speed $\omega$. Given the mass $m$ and moment of inertia $I_z$. Is it possible to calculate the angular velocity?

Homework Equations

Not sure what we need, but I believe it's going to involve energy.
$K_{rot}=\frac{1}{2}I_z\omega^2$
Other than that I'm not sure.

The Attempt at a Solution

No idea. I've been thinking about the problem for the past couple days but can't figure out how to determine the angular velocity given only these variables. If needed I may be able to supply other variables (this is a overly simplified example to give you an idea of the problem).

Thanks.

 

[ehild]

I have no idea about this problem without a picture... ehild

 

[lanew]

Sorry about that, here's a quick sketch:

http://imageshack.us/photo/my-images/192/selection005e.png/

 

[ehild]

Applying that constant tangential force F means constant torque (τ=R*F) with respect to the fixed axis and constant angular acceleration: β=τ/I, where I is the moment of inertia, again with respect to he fixed axis. The angular velocity will change with time.

ehild

 

[asteriatic]

I would suggest starting by reviewing the fundamental principles of rotational motion and rigid body dynamics. These principles include the conservation of angular momentum and the relationship between torque and angular acceleration. Additionally, the equations of rotational motion, such as the one you mentioned for rotational kinetic energy, can be used to solve for the angular velocity in this problem. It may also be helpful to draw a free body diagram and apply the equations of motion to the individual components of the system (shaft and cross member). With the given variables, it is possible to calculate the angular velocity by setting up and solving the appropriate equations. If you are still having trouble, I recommend consulting a textbook or seeking help from a tutor or instructor.