Calculate the moment of inertia

In summary: Be sure to read and understand the homework posting guidelines and show all your work.In summary, a mass m is released from rest and falls a distance S after time t. The mass is tied to an axle fixed at a wall, with a radius of r. With no friction present, the moment of inertia of the axle can be represented by the equation 0.5Iω^2. By using the equations v=at, S=0.5at^2, and the definition of torque T=Iω, we can solve for the moment of inertia in terms of m, r, t, and S.
  • #1
asdff529
38
0

Homework Statement


A mass m is tied with a light string,which it's another end is winded at a axle fixed at wall,in which it's radius is r.
Assume there is no friction.The mass is released from rest and falls a distance S after time t.
Find the moment of inertia of the axle.(represents I in terms of m,r,t and S)

Homework Equations


work done by moment=0.5Iω^2
v=at
S=0.5at^2

The Attempt at a Solution


my final equation is as follows
TS=0.5Iω^2,where T is the tension
v=at=rαt where α is the angular acceleration
(mg-T)S=0.5mv^2
but i can't reach the requirement
maybe there are lots of error inside and sorry for my poor english
 
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  • #2
Try solving for v and ω.
 
  • #3
A mass m is tied with a light string,which it's another end is winded at a axle fixed at wall,in which it's radius is r.
Assume there is no friction.The mass is released from rest and falls a distance S after time t.
Find the moment of inertia of the axle.(represents I in terms of m,r,t and S)
well let's look at what's happening...
You have a mass on an axel, and you release it, the Earth (gravity) exerts a torque of ##T = I\dot{\omega}## on the axel and it accelerates angularly at a rate of ##\dot{\omega}##

So I guess what it boils down to is this: how else can you define ##T##?
There's another definition that involves 2 things that you are given (variables) and a constant that you know.

Answer this and we'll go from there.

PS I like this problem =]
 
  • #4
There are several ways to solve this. There is nothing wrong with the original approach using work and energy. The only thing to realize is that v and ω are not unknowns--a little kinematics is all you need to find them.
 
  • #5
i almost forgot i can use the formula v^2-u^2=2as
so v=sqrt(2rαS) ?
and ω=αt or ω=v/R
am i going right?
 
  • #6
what's u?
Also you're over complicating it in my opinion.
Start out with what you know, write out some definitions, and when in doubt: N2L is god.
 
  • #7
asdff529 said:
i almost forgot i can use the formula v^2-u^2=2as
so v=sqrt(2rαS) ?
and ω=αt or ω=v/R
am i going right?
First step is to find the acceleration. You had the formula in your first post.
asdff529 said:
S=0.5at^2

Then find v. Again, you had the formula in your first post.
asdff529 said:
v=at

Given v, you can find ω since they are related.

Then you can use the energy equations you wrote in your first post.
 

What is the moment of inertia?

The moment of inertia is a measure of an object's resistance to rotational motion. It is similar to mass in linear motion, but instead describes an object's resistance to rotational acceleration.

How is the moment of inertia calculated?

The moment of inertia can be calculated by multiplying the mass of an object by the square of its distance from the axis of rotation. For more complex objects, the moment of inertia can be found by integrating the mass distribution of the object with respect to the axis of rotation.

What are the units of moment of inertia?

The units of moment of inertia are typically kg*m^2 (kilogram meters squared) in the SI system. Other common units include g*cm^2 (gram centimeters squared) and oz*in^2 (ounces inches squared).

How does the moment of inertia affect an object's rotational motion?

A larger moment of inertia will result in a slower rotational motion, as it requires more torque to overcome the object's resistance to rotation. Conversely, a smaller moment of inertia will result in a faster rotational motion.

Can the moment of inertia be negative?

No, the moment of inertia is always a positive value. It represents an object's resistance to rotation and cannot be negative. However, it can be zero for objects with no mass or objects that are rotating about their axis of symmetry.

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