Moment of Inertia hw problem

In summary, two metal disks with different radii and masses are welded together and mounted on a frictionless axis. The total moment of inertia of the two disks can be calculated using the formula I = Σ mi *ri^2. A light string is wrapped around the smaller disk and a block is suspended from the end of the string. The speed of the block just before it strikes the floor can be found using the equation m*g*h = 1/2 *I*ω^2, taking into account the kinetic energy of the block. However, it is important to use the correct formula for moment of inertia, which is 0.5MR^2 for a solid cylindrical disk.
  • #1
jhwatts
5
0

Homework Statement



2 metal disks, one with radius R1= 2.5cm and mass M1=.8kg and the other with radius R2=5.00cm and mass M2=1.60kg, are welded together and mounted on a frictionless axis through their common center.

a)What is the total moment of inertia of the two disks?
b)A light string is wrapped around the edge of the small disk, and a 1.5kg block, suspended from the free end of the string. If the blook is 2.00m above the floor what is the speed of just before it strikes the floor?


Homework Equations


I = Σ mi *ri^2
K = 1/2 *I*ω^2
W(g)= m*g*h


The Attempt at a Solution


a) I = 0.8kg*(2.5cm)^2 +1.6kg(5.00cm)^2 = 45kg*cm = .0045kg*m

b) m*g*h = 1/2 *I*ω^2
i) 1.5kg*9.8m/s^2*2m = .5*(.0045kg*m) * ω^2
ii) ω = sqrt[(1.5kg*9.8m/s^2*2m ) / (.5*(.0045kg*m))]

This is what i thought i should do, but looking at the solution in the back of the book, i doesn't seem to be correct. Any help is appericated, thanks.
 
Last edited:
Physics news on Phys.org
  • #2
If you are going to use energy methods, I think you need to account for the ke of the falling block as well. In other words some of its potential energy of the block goes into rotating the flywheel and some into its own motion. Also I think you dropped a factor of 2m in "1)"
 
  • #3
Ture, that was just a copy error though from my paper to the computer.
In part a. my book says the answser should be have of what i calculated it to be, do you know why that might be?
 
Last edited:
  • #4
jhwatts said:
In part a. my book says the answser should be have of what i calculated it to be, do you know why that might be?
You are using the wrong formula for the moment of inertia of a solid cylindrical disk. It is 0.5MR^2, not MR^2, which is what you are using.
 
Last edited:
  • #5
Thanks i figured it out when i was reading my book, and i figured out why my velocity calcuation was coming out wrong i forgot to add the KE of the weight. Thanks for your help.
 
  • #6
I am doing this question, and I am using Conservation of Energy and the following equation:

mgh = 0.5*I*(v^2/r^2)+0.5*m*v^2, which I then arrange:

2mgh = v^2((I/(r^2))+m)

v^2 = (2mgh)/((I/r^2)+m)

but cannot get the right answer when I put in the variables. Any Ideas why?



TFM
 
Last edited:

1. What is moment of inertia and how is it related to a hw problem?

Moment of inertia is a measure of an object's resistance to rotational motion. In a hw problem, it is used to calculate the rotational kinetic energy of an object.

2. How is moment of inertia different from mass?

Mass is a measure of an object's resistance to linear motion, while moment of inertia is a measure of its resistance to rotational motion. They are related by the object's shape and distribution of mass.

3. How do I calculate moment of inertia for a given object?

The moment of inertia depends on the object's shape and mass distribution. For simple objects, such as a rod or a sphere, there are known formulas that can be used. For complex objects, it may require integration to calculate the moment of inertia.

4. What is the unit of measurement for moment of inertia?

The unit of moment of inertia depends on the unit of mass and the unit of distance used. In SI units, it is measured in kilograms per meter squared (kg/m^2).

5. How does moment of inertia affect the rotational motion of an object in a hw problem?

Moment of inertia plays a crucial role in determining the rotational motion of an object. A higher moment of inertia means that more energy is required to rotate the object, resulting in slower rotational motion. On the other hand, a lower moment of inertia means that less energy is required, resulting in faster rotational motion.

Similar threads

  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
806
  • Introductory Physics Homework Help
Replies
28
Views
482
  • Introductory Physics Homework Help
Replies
8
Views
996
  • Introductory Physics Homework Help
Replies
8
Views
7K
  • Introductory Physics Homework Help
Replies
4
Views
996
  • Introductory Physics Homework Help
Replies
8
Views
975
  • Introductory Physics Homework Help
Replies
7
Views
238
  • Introductory Physics Homework Help
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
3K
Back
Top