Uniform roating disk - find inertia

[mattmannmf]

A uniform disk of mass Mdisk = 4 kg and radius R = 0.22 m has a small block of mass mblock = 2.1 kg on its rim. It rotates about an axis a distance d = 0.17 m from its center intersecting the disk along the radius on which the block is situated.

a) What is the moment of inertia of the block about the rotation axis?

b) What is the moment of inertia of the disk about the rotation axis?

c) When the system is rotating about the axis with an angular velocity of 4.5 rad/s, what is its energy?

d) If while the system is rotating with angular velocity 4.5 rad/s it has an angular acceleration of 8.1 rad/s2, what is the magnitude of the acceleration of the block?

Im just stuck on everything for this problem. For A. I tried m*r^2 (2.1*.17^2) that was wrong...i just don't know how to start. I tried applying the inertia formula solid cylinder: .5*M*r^2 but it came out wrong. Dont know what I am doing wrong.

 

[tiny-tim]

Welcome to PF!

Hi mattmannmf ! Welcome to PF!

(try using the X² tag just above the Reply box )

A uniform disk of mass Mdisk = 4 kg and radius R = 0.22 m has a small block of mass mblock = 2.1 kg on its rim. It rotates about an axis a distance d = 0.17 m from its center intersecting the disk along the radius on which the block is situated.

a) What is the moment of inertia of the block about the rotation axis?

b) What is the moment of inertia of the disk about the rotation axis?
…
For A. I tried m*r^2 (2.1*.17^2) that was wrong...i just don't know how to start. I tried applying the inertia formula solid cylinder: .5*M*r^2 but it came out wrong. Dont know what I am doing wrong.

For a), you're right, except you should be using R - 0.17

For b), use the parallel axis theorem I = I_C + md², where I_C is the moment of inertia about a parallel axis through the centre of mass, and d is the (perpendicular) distance between the axes.

 

[mattmannmf]

ahh! thanks for a

Now for be, parallel axis theorem.
I= Ic + md^2

Is Ic= .5*m*r^2 (where m=4, r=.22)
2nd part is just adding on the answer from part a?

 

[tiny-tim]

HI mattmannmf!

(just got up :zzz: …)

Now for be, parallel axis theorem.
I= Ic + md^2

Is Ic= .5*m*r^2 (where m=4, r=.22)
2nd part is just adding on the answer from part a?

Yes, I_c= .5*m*r².

How can you add on the answer from part a? part a is for the block, part b is for the disc.

 

[mattmannmf]

well for the md^2
m= mass of disk (4)
d= .17

I am a bit confused of what the whole point of md^2 means? Ic is the inertia of the disk, but what does the md^2 come in?

 

[tiny-tim]

I am a bit confused of what the whole point of md^2 means? Ic is the inertia of the disk, but what does the md^2 come in?

ohhh.

I assumed you would look up "parallel axis theorem" in your book or your notes or wikipedia or just google it if you didn't know what it was.

You certainly need this information for your exams, so you'd better look it up now.

 

[mattmannmf]

Ic is the moment of inertia of the object about its center of mass;
M is the object's mass;
D is the perpendicular distance between the two axes.

Ok so M is the objects mass, does that mean the mass of just the disk? or the total mass of the system (disk + block)?
D is the distance between 2 axes which means its .17m

 

[tiny-tim]

Ok so M is the objects mass, does that mean the mass of just the disk? or the total mass of the system (disk + block)?
D is the distance between 2 axes which means its .17m

Hi mattmannmf!

Yes, d is .17m.

And M is the mass of the same thing that has the centre of mass at C …

so in this case, it must be … ? ​

 

[mattmannmf]

its the disk