Moment of inertia of four point masses about x, y, and z axes

[huybinhs]

Homework Statement

Four point masses are arranged on the xy plane as follows.

Mass1 = 27.0 grams at x = 2.00 cm and y = 2.00 cm.

Mass2 = 31.0 grams at x = 0.00 cm and y = 4.00 cm.

Mass3 = 49.0 grams at x = -3.00 cm and y = -3.00 cm.

Mass4 = 31.0 grams at x = -1.00 cm and y = 2.00 cm.

a) What is the rotational inertia if this collection of masses is rotating about the x axis?

b) What is the rotational inertia if this collection of masses is rotating about the y axis?

c)What is the rotational inertia if this collection of masses is rotating about the z axis?

Homework Equations

I = mr²

The Attempt at a Solution

I need to change to the right units:

Mass 1 = 0.027 kg at x = 0.02 m and y = 0.02 m

Mass 2 = 0.031 kg at x = 0.00 m and y = 0.04 m

Mass 3 = 0.049 kg at x = -0.03 m and y = -0.03 m

Mass 4 = 0.031 kg at x = -0.01 m and y = 0.02 m

Now I know each mass, and converted to the right units. What should I do next? Thanks!

 

[fzero]

The moment of inertia about an axis is

$$I = \sum_i m_i r_i^2,$$

where $$r_i$$ is the distance from the point $$i$$ to the axis of rotation. For each part you will need to compute the distances from each mass to the relevant axis of rotation and then compute that sum. It will probably help to draw a picture for yourself.

 

[huybinhs]

The moment of inertia about an axis is

$$I = \sum_i m_i r_i^2,$$

where $$r_i$$ is the distance from the point $$i$$ to the axis of rotation. For each part you will need to compute the distances from each mass to the relevant axis of rotation and then compute that sum. It will probably help to draw a picture for yourself.

Ok, so on mass 1, we have x = 0.02 m and y = 0.02m. Therefore we the mass on those point (0.02, 0.02), so how can I find r_i ?

 

[fzero]

Ok, so on mass 1, we have x = 0.02 m and y = 0.02m. Therefore we the mass on those point (0.02, 0.02), so how can I find r_i ?

The value of r_i depends on which axis of rotation you are considering. It's best to draw a picture in the x-y plane with all of the points on it. Then you'll be able to just read off the distances from the x and y axes. For the z axis you can use the Pythagorean formula.

 

[huybinhs]

The value of r_i depends on which axis of rotation you are considering. It's best to draw a picture in the x-y plane with all of the points on it. Then you'll be able to just read off the distances from the x and y axes. For the z axis you can use the Pythagorean formula.

Could u give an example on mass 1 please!