# A uniform cyclinder made of lead has the same mass and the same length as a uniform solid cylinder made of wood. The rotatonal inertia of the lead cylinder compared to the wooden one is:

I thought at first that the rotational inertia cannot be known or compared because we need the radius information to make a judgement. But then I went through the equations a solid cyclinder is I= 1/12 ML^2. So they would both be the same because we know the mass and length are the same.

To increase the rotational inertia of a solid disk about it axis without changing its mass:
a) drill holes near the rim and put the material near the axis
b) drill holes near the axis and put the material near the rim
c) drill holes at points on a circle near the axis and put the material between the holes.
e) none of the above (rotation inertia cannot be changed without changing the mass)

I think the answer is b. Drill a whole near the axis and move the material near the rim because inertia is increased when the mass is distributed farther from the axis.

You are formula shopping....The formula you cite 1/12 ml^2 is not it.

I depends on how mass is distributed, and RADIUS. THe masses of lead and wood are considerably of differing density, so the wood will have much greater radius.

On the second, b is correct.

10 years ago

8 months ago

8 months ago

## I apologize for the confusion caused by the incorrect formula I mentioned earlier. You are correct that the rotational inertia of a cylinder depends on the distribution of mass and the radius. Since the masses are the same and the question states that the length is also the same, we can assume that the radius of the lead cylinder is smaller than that of the wooden cylinder in order to have the same mass. Therefore, the rotational inertia of the lead cylinder would be smaller compared to the wooden cylinder.

For the second question, you are correct again. To increase the rotational inertia of a solid disk without changing its mass, we can drill holes near the axis and move the material (mass) near the rim. By doing this, we are redistributing the mass farther from the axis, which increases the rotational inertia. So the correct answer is option b) drill holes near the axis and put the material near the rim.