How Is the Moment of Inertia Constant Determined Experimentally?

In summary, the conversation discusses a lab on energy of a rolling object and deriving the constant (k) in the equation for moment of inertia. The participants suggest making a graph of x^2 vs h and calculating k from the slope of the trendline. They also mention the theoretical value of k=1 for a hollow cylinder and discuss their attempts at finding the slope.
  • #1
stalebrownie
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Homework Statement


For a little background, this lab was on energy of a rolling object. We rolled a hollow cylinder from the top of a ramp on a table and onto the floor. We are trying to experimentally derive the constant (k) found in the equation for moment of inertia.

Variables: h = height from top of ramp to table, H = height from table to floor, x = distance ball travels from end of ramp to its landing on floor

Make a graph of x^2 vs h. Add a trendline. Calculate k from the slope of the trendline as it corresponds to x^2 = (4Hh)/(k+1)

My trendline equation is x^2 = 1.98h - .086

Homework Equations



I = kmr^2
x^2 = (4Hh)/(k+1)
We know theoretically that k=1 for a hollow cylinder

The Attempt at a Solution


At first I thought the slope was k but that doesn't make sense because my expected k is 1.
I could just calculate k given my experimental measurements, but that's not what they're asking. I'm trying to relate the given equation to mx+b form but I'm drawing a blank. I don't know how to start.

Thanks!
 
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  • #2
You have x2 = (4Hh)/(k+1) ⇒ x2 = (4H/(k+1)) h

this is in the form Y=MX+C, Y=x2 and X=h. What is M?
 

Related to How Is the Moment of Inertia Constant Determined Experimentally?

1. What is the moment of inertia constant?

The moment of inertia constant, also known as the mass moment of inertia, is a physical constant that describes an object's resistance to changes in its rotational motion. It is a measure of how an object's mass is distributed around its axis of rotation.

2. How is the moment of inertia constant calculated?

The moment of inertia constant is calculated by multiplying the mass of an object by the square of its distance from its axis of rotation. This calculation takes into account the distribution of mass around the axis of rotation and is different for each axis.

3. What are the units of the moment of inertia constant?

The moment of inertia constant has units of mass times length squared (kg∙m2 or slug∙ft2). This is because it is derived from the basic units of mass and length, and the squared length takes into account the distribution of mass around the axis of rotation.

4. How does the moment of inertia constant affect an object's motion?

The moment of inertia constant plays a crucial role in an object's rotational motion. A larger moment of inertia constant means it will be more difficult to change an object's rotational speed, as more force is required to overcome its inertia. This is why objects with larger moment of inertia constants, such as a spinning top, tend to rotate for longer periods of time.

5. Can the moment of inertia constant be changed?

Yes, the moment of inertia constant can be changed by altering an object's mass distribution or its axis of rotation. For example, a figure skater can change their moment of inertia by extending their arms (increasing their mass distribution) or pulling them in (decreasing their mass distribution). This change in moment of inertia affects their rotational speed and allows them to perform different spins and jumps.

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