Do Rotational Inertia Calculations Require Integration?

[blackout85]

First questionThree identical balls, with masses M, 2M, and 3M are fastened to a massless rod of length L as shown. The rotational inertia about the left end of the rod is: Thats the layout below. Would calculus be needed in this problem (intergration) because then I am in trouble. I know the rotation at the end of rod is I=ML^2/3. Could I use that formula.

3M-----L/2----2M----L/2-----M

work:
I came up with an answer of 3ML^2/2
does that look right. I added the two end mass and lengths using the equation I=mr^2--> simply plugging in the values and adding. Would that be correct.

second question:
If a wheel turns with a costant rotational speed then: each point on its rim moves with constant roational velocity, each point on its rim moves with constant translational acceleration, the wheel turns with constant translation acceleration, the wheel turns through equal angles in equal times, the angle through which the wheel turns in each second increases as time goes on, the angle through which the wheel turns in each second decreases as time goes on.

work
I thought if the wheel turns with a constant translational velocity along the rim because of the the equation v=wr. Am I right to think since along the rim will have the same radius as in a wheel.

I would appreciate any feedback on both questions. Thank you

 

[Hootenanny]

The answer to your first question is correct. With regards to the second question, is that copied directly from your text or have you paraphrased it?

 

[blackout85]

physics

I rechecked it
If a wheel turns with a constant rotational speed:
each point on its rim moves with a constant translational velocity
each point on its rim moves with a constant translational acceleration
the wheel turns through equal angles in equal times
the angle through which the wheel turns in each second increases as times goes on
the angle through which the wheel turns in each second decreases as time goes on

work:
I thought if the wheel turns with a constant translational velocity along the rim because of the the equation v=wr. Am I right to think since along the rim will have the same radius as in a wheel. This equation connects rotational velocity to translational velocity. Since the radius is the same for the edge in a wheel I thought that the answer is constant translational velocity.

 

[Hootenanny]

You are indeed correct. Although there is one further choice which is also correct...