Inertia moments (i don't know)

In summary, the conversation discusses the confusion surrounding the use of torque and conservation of energy in basic angular motion. The speaker questions why they cannot use the formula Torque=Ia to solve for the moment of inertia of a pulley with an unknown mass, while also considering conservation of energy. However, it is pointed out that this formula assumes the force exerted on the pulley equals the weight of the hanging mass, which is not always the case. This leads to different answers when solving for the moment of inertia.
  • #1
kp
53
0
once again I have succeeded in confusing myself about basic angular motion...:confused:

If I have a pulley of with an unkown moment of inertia, and a bucket hanging from the pulley with a known mass, height, and acceleration in which it falls. Why can't i use:

Torque = Ia
rf = Ia
r * mg = Ia
r*mg/a = I

or can I, because when i use conservation of energy

mgh = 1/2mv^2 + 1/2Iw^2 and solve for I, i get different answers.

:grumpy:
 
Physics news on Phys.org
  • #2
kp said:
Torque = Ia
rf = Ia
r * mg = Ia
r*mg/a = I
This assumes that the force exerted on the pulley equals the weight of the hanging mass. Not true. The force does equal the tension in the cord. (If the force exerted on the pulley equalled the weight of the hanging mass, then by Newton's 3rd law the mass would be in equilibrium.)
 
  • #3


It is completely understandable to feel confused about basic angular motion. Inertia moments, also known as moments of inertia, refer to an object's resistance to rotational motion. This means that the moment of inertia of an object depends on its mass distribution and the axis of rotation.

In the example you have provided, you are trying to calculate the moment of inertia of a pulley using the equation Torque = Ia. While this equation is correct, it only applies in certain situations where the axis of rotation is fixed and the object is rotating about that axis. In your case, the pulley is not rotating about a fixed axis, but rather the bucket is falling due to gravity. Therefore, this equation cannot be used to calculate the moment of inertia of the pulley.

When using conservation of energy to solve for the moment of inertia, it is important to consider all forms of energy involved. In your equation, you have only accounted for the potential and kinetic energy of the bucket, but you have not included the rotational energy of the pulley. This is why you are getting different answers when solving for I.

To accurately calculate the moment of inertia of the pulley, you will need to consider the rotational energy of the pulley as well. This can be done by using the equation you mentioned, mgh = 1/2mv^2 + 1/2Iw^2, where w is the angular velocity of the pulley. By including this additional term, you should be able to obtain a more accurate value for the moment of inertia of the pulley.

I hope this helps clear up your confusion. Keep in mind that angular motion can be complex, and it is always important to consider all factors and forms of energy involved when solving for values such as moment of inertia.
 

What is an inertia moment?

An inertia moment, also known as a moment of inertia, is a measure of an object's resistance to changes in its rotational motion. It is similar to mass in linear motion, but instead measures an object's resistance to rotational acceleration.

How is inertia moment calculated?

The inertia moment of an object is calculated by multiplying the mass of the object by the square of its distance from the axis of rotation. The formula is I = mr², where I is the moment of inertia, m is the mass, and r is the distance from the axis of rotation.

What is the significance of inertia moments?

Inertia moments are important in understanding the behavior of rotating objects, such as wheels, flywheels, and propellers. They also play a crucial role in engineering, as they help determine the stability and efficiency of structures and machines.

How does inertia moment affect rotational motion?

Inertia moment affects rotational motion by determining how much torque is required to change the object's rotational speed. Objects with larger moments of inertia will require more torque to rotate, while objects with smaller moments of inertia will require less torque.

Can inertia moment be changed?

Yes, inertia moment can be changed by altering the mass or distribution of mass in an object. For example, a wheel with a heavier rim will have a larger moment of inertia than a wheel with a lighter rim. Additionally, the shape and size of an object can also affect its inertia moment.

Similar threads

  • Introductory Physics Homework Help
Replies
13
Views
1K
  • Introductory Physics Homework Help
Replies
11
Views
250
  • Introductory Physics Homework Help
Replies
8
Views
7K
  • Introductory Physics Homework Help
Replies
28
Views
483
Replies
25
Views
374
  • Introductory Physics Homework Help
Replies
10
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
240
  • Introductory Physics Homework Help
Replies
5
Views
920
  • Introductory Physics Homework Help
Replies
1
Views
847
  • Introductory Physics Homework Help
Replies
8
Views
997
Back
Top