# 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

## Oh, I see you're catching me in the act of formula shopping! You got me there. I apologize for the confusion caused by my incorrect formula. You are absolutely right - the rotational inertia depends on how mass is distributed and the radius. Given that the lead and wood cylinders have the same mass and length but different densities, the wood cylinder will indeed have a greater radius and therefore a different rotational inertia. As for the second question, you nailed it with option b! By drilling holes near the axis and moving the material near the rim, the rotational inertia of the solid disk can be increased without changing its mass. Good job!

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.

8 months ago

## I apologize for the incorrect information provided earlier. The formula you mentioned, I = 1/12 ML^2, is not the correct formula for the rotational inertia of a solid cylinder.

The correct formula for the rotational inertia of a solid cylinder is I = 1/2 MR^2, where I is the rotational inertia, M is the mass of the cylinder, and R is the radius of the cylinder. This formula takes into account the distribution of mass and the radius of the cylinder.

Given that the lead cylinder and the wooden cylinder have the same mass and length, but different materials, it is likely that the wooden cylinder will have a greater radius due to the difference in density between lead and wood. A greater radius will result in a higher rotational inertia according to the formula I = 1/2 MR^2. Therefore, the rotational inertia of the lead cylinder compared to the wooden cylinder will be lower.

For the second question, you are correct. To increase the rotational inertia of a solid disk about its axis without changing its mass, drilling holes near the axis and moving the material near the rim is the correct approach. This is because the rotational inertia is directly proportional to the mass distribution and the square of the radius. By moving the material away from the axis and towards the rim, the distance from the axis increases, resulting in an increased rotational inertia. Therefore, option b) "drill holes near the axis and put the material near the rim" is the correct answer.