How is rotational inertia effected by weight if at all? I am designing wheels and I'm considering the load placed on these wheels. I am not sure if the mass of the load should be incorperated into the inertia at all. Thanks!
Think of a cart on wheels... the cart has some given mass and I want to know what's the relationship between the mass of the cart and the inertia of the wheels. I know the weight is dstributed evenly to the wheels, but i get stuck when it comes to the inertia, wether weight affects it or not
Maybe I'm still not getting it, but let me throw some things out there. Hopefully some others with more Newtonian Mechanics than I will chime in and shed some light. This looks like this could be a multi-faceted Mechanics problem, although I'm still having trouble understanding the exact problem.
1. I see the rotating wheel having rotational inertia
2. I see the "same" rolling wheel having inertia in the direction of travel
3. The first sentence asks "How is rotational inertia effected by weight if at all?"
Ill assume the "load" placed on these wheels is like the body of a car, or the body of a motorcyle, 4 or two wheels respectively. This coupling, or connecting to the wheels changes many things from a Classical Mechanics perspective.
If the car body was nearly zero in mass, and the car traveling in a straight line, I think the "coupled",(two or more wheels tied together), rotational inertia would be minimally effected.
If the car body was large in mass, the wheels rotational inertia would have only a small effect on the vehicle.
There are many variables possible in your question. I believe the answer could vary wildly given the adjustment of certain variables.
4. "mass of the load should be incorperated into the inertia at all" I'm scratching my head with this statement. Is it saying to alter the wheel's inertia,(by changing wheel design), if the cars mass has a significant influence?
5. What is the "goal" of the wheel design? , performance? gas miledge for a given mass?
Maybe I'm over analyzing the problem, hopefully I have been some help, perhaps someone will shed some light on this problem for both of us.
sry, I forget how specific you sometimes need to get with problems. Using the inertia of a cylinder, the equation is I = 1/2 * M(R^2) . Now that is for just the cylinder. What I am trying to figure out is if the mass of the load will sneak itself into the equation or will it be an outside factor that i will need to account for. And this mass is relatively signifcant. Approx. 114 kg on 4 wheels with radius 5.08 cm ( 2 in) and the wheels have a mass of 2 kg each.
Only the mass of the wheel is important when calculating the moment of inertia of each wheel. You need to worry about the mass of the load when calculating the movement of the entire cart.