Calculating the moment of inertia in a pulley system

[mldavis086]

Homework Statement

An object with a mass of m = 5.10 kg is attached to the free end of a light string wrapped around a reel of radius R = 0.250 m and mass M = 3.00 kg. The reel is a solid disk, free to rotate in a vertical plane about the horizontal axis passing through its center. The suspended object is released from rest 6.00 m above the floor. Determine
(a) the tension in the string,
(b) the acceleration of the object, and
(c) the speed with which the object hits the fl oor.
(d) Verify your answer to (c) by using the isolated system (energy) model.

Homework Equations

The Attempt at a Solution

I don't expect you to answer the whole question but just this part would be great!

When calculating the moment of inertia, I have the formula to be I = Ʃ m*r^2

They show how to get the answer in the book but I don't understand it. When they calculate the moment of inertia, they have (1/2)(3)(0.25)^2

Where did the half come from? This is a new chapter in the book and I'm not sure I even really get what the moment of inertia is. If anyone can help me it would be greatly appreciated

 

[tiny-tim]

hi mldavis086 !

… The reel is a solid disk …
…
When calculating the moment of inertia, I have the formula to be I = Ʃ m*r^2

They show how to get the answer in the book but I don't understand it. When they calculate the moment of inertia, they have (1/2)(3)(0.25)^2

Where did the half come from?

ah, you need to learn the moment of inertia of the common shapes (see eg http://en.wikipedia.org/wiki/List_of_moments_of_inertia)

for a disc (ie a cylinder), about its axis, it's 1/2 mr²

 

[mldavis086]

That's great. Thanks!