Moment of Inertia Problems and Conservation of Energy

In summary, the conversation discusses using conservation of energy laws to determine the speed of a mass on the right when it hits the ground. The speaker mentions using the alpha of the pulley to calculate the system's acceleration, but wants to know how to do it using conservation of energy. They also mention comparing the total mechanical energy of the system before and after the mass falls. They suggest setting up a conservation equation and including the potential and kinetic energy of both masses and the pulley. The speaker hints at expressing all kinetic energy terms in terms of the speed of block B to solve for its speed without using force equations or kinematics.
  • #1
Lancelot59
646
1
I have this situation here:

GIANCOLI.ch10.p067.jpg


I'm given the masses for the objects, as well as the radius and mass of the pulley. I have to use conservation of energy laws to find out how fast the mass on the right is going the instant it hits the ground.

I can find out what the alpha of the pulley is, and therefore the accelration of the system, but that's just kinematics. How can I use conservation of energy to do it?

How could I do it if the pulley was ideal?
 
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  • #2
Lancelot59 said:
How can I use conservation of energy to do it?
Compare the total mechanical energy of the system before and after the mass falls.
 
  • #3
I don't follow...

I see that there is none before, and some after, when the block b has zero potential energy, block A has potential and kinetic energy, and the pulley has rotational kinetic energy...but if I knew those values then I could just save the trouble and use kinematics.
 
  • #4
Set up a conservation equation:
KE1 + PE1 = KE2 + PE2

Make sure you include the PE and KE of both masses and the pulley. You'll be able to solve for the speed of block B without using force equations or kinematics. Hint: Express all the KE terms in terms of the speed of block B.
 

1. What is the moment of inertia and how is it calculated?

The moment of inertia is a measure of an object's resistance to rotational motion. It is calculated by multiplying the mass of the object by the square of its distance from the axis of rotation.

2. How does the moment of inertia affect the motion of an object?

The moment of inertia determines how much torque is needed to accelerate or decelerate an object's rotational motion. Objects with a larger moment of inertia will be more difficult to accelerate, while objects with a smaller moment of inertia will be easier to accelerate.

3. What is the relationship between moment of inertia and conservation of energy?

The moment of inertia is directly related to the conservation of energy in rotational motion. As the moment of inertia increases, so does the kinetic energy of the object. This means that more energy is required to change the rotational motion of an object with a larger moment of inertia.

4. How do you solve moment of inertia problems?

To solve moment of inertia problems, you will need to know the mass and dimensions of the object, as well as the axis of rotation. You will also need to apply the correct formulas for calculating moment of inertia, taking into account the shape and distribution of mass of the object.

5. Can the moment of inertia of an object change?

Yes, the moment of inertia of an object can change if the mass or dimensions of the object change, or if the axis of rotation is moved. Additionally, the moment of inertia can be affected by the distribution of mass within an object, with more mass concentrated farther from the axis of rotation resulting in a larger moment of inertia.

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