Calculating Moment of Inertia for a Pulley with Attached Mass

In summary, the conversation discusses finding the moment of inertia of a pulley with a mass attached to it and a light cord. The person initially tried to use the equation I=mr^2 but it did not work. They then attempted to find the torque using T=mgr and dividing it by the acceleration and radius, but it gave them the wrong answer. They ultimately found the correct solution using a different set of equations.
  • #1
Keithkent09
33
0

Homework Statement


A 1.65 kg mass is attached to a light cord that is wrapped around a pulley of radius 4.65 cm, which turns with negligible friction. The mass falls at a constant acceleration of 2.40 m/s2. Find the moment of inertia of the pulley.

Homework Equations


I=mr^2
Torque=I*alpha


The Attempt at a Solution


I tried to just square the radius given and multiply it by the mass but that did not work. I also tried to find the Torque using T=mgr. And then divided that number by the acceleration/radius in order to get the angular acceleration.
 
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  • #2
Keithkent09 said:
I also tried to find the Torque using T=mgr. And then divided that number by the acceleration/radius in order to get the angular acceleration.

So what did that give you?
 
  • #3
It gave me the wrong answer. I guess that is not the correct way to find the torque
 
  • #4
Keithkent09 said:
It gave me the wrong answer. I guess that is not the correct way to find the torque

That should be the correct way to do it, post your work.
 
  • #5
I figured it out using a different set of equations. Thanks for your help though, sorry to waste your time.
 
  • #6
Keithkent09 said:
I figured it out using a different set of equations. Thanks for your help though, sorry to waste your time.

What equations did you use by chance?
 

FAQ: Calculating Moment of Inertia for a Pulley with Attached Mass

What is moment of inertia?

Moment of inertia is a physical property of an object that measures its resistance to changes in rotational motion. It is a measure of how mass is distributed around an axis of rotation.

How is moment of inertia of a pulley calculated?

The moment of inertia of a pulley is calculated as the product of the mass of the pulley, the radius of the pulley, and the square of the radius. It can also be calculated using the formula I = MR^2, where I is the moment of inertia, M is the mass of the pulley, and R is the radius of the pulley.

Why is moment of inertia important for a pulley?

Moment of inertia is important for a pulley because it affects the pulley's ability to store and release rotational energy. It also plays a crucial role in determining the pulley's acceleration and the amount of force needed to move the pulley.

How does the shape of a pulley affect its moment of inertia?

The shape of a pulley affects its moment of inertia because it determines how the mass is distributed around its axis of rotation. A pulley with a larger radius or a larger mass will have a higher moment of inertia compared to a pulley with a smaller radius or a smaller mass.

How does the moment of inertia of a pulley affect its mechanical advantage?

The moment of inertia of a pulley affects its mechanical advantage because it determines the amount of force needed to move the pulley and the resulting acceleration. A pulley with a higher moment of inertia will require more force to move, resulting in a lower mechanical advantage.

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