Moment of Inertia of a Pendulum

In summary: Sorry for bumping up an old thread, but thought it'd be better than making a new one about the same problem. Can someone tell me where equation for I is derived from? From my knowledge I know that I = cMR^2 (as an estimated value), but what exactly do you plug into get to that point? (I = mgLT^2/4pi^2 )Hi, The equation for I is derived from the moment of inertia of the weight, mg, and the length of the weight, L, and the tension in the spring, T.
  • #1
MyNewPony
31
0

Homework Statement



The 20 cm-long wrench in the figure swings on its hook with a period of 0.92s. When the wrench hangs from a spring of spring constant 350 N/m, it stretches the spring 3.5 cm.

What is the wrench's moment of inertia about the hook?

http://session.masteringphysics.com/problemAsset/1070606/9/14.EX25.jpg

Homework Equations



I = m*g*L*T^2/2pi

The Attempt at a Solution



Fsp = Fg
kx = mg
m = kx/g
m = (350)(0.035)/9.8 = 1.25

I = (1.25)(9.8)(0.14)(0.92)^2/2pi = 0.23 kg*m^2

This isn't the correct answer however. Can someone explain what I did wrong?
 
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  • #2
Hi MyNewPony,

MyNewPony said:

Homework Statement



The 20 cm-long wrench in the figure swings on its hook with a period of 0.92s. When the wrench hangs from a spring of spring constant 350 N/m, it stretches the spring 3.5 cm.

What is the wrench's moment of inertia about the hook?

http://session.masteringphysics.com/problemAsset/1070606/9/14.EX25.jpg

Homework Equations



I = m*g*L*T^2/2pi

This formula does not look quite right to me. Do you see what it needs to be?
 
  • #3
alphysicist said:
Hi MyNewPony,



This formula does not look quite right to me. Do you see what it needs to be?

Ah. I forgot to square the 2pi.

So the equation becomes:

I = mgLT^2/4pi^2

Is that correct?
 
  • #4
MyNewPony said:
I = m*g*L*T^2/2pi
This equation isn't quite right. It's off by a factor of 2pi.
 
  • #5
MyNewPony said:
Ah. I forgot to square the 2pi.

So the equation becomes:

I = mgLT^2/4pi^2

Is that correct?

That looks right to me.
 
Last edited:
  • #6
MyNewPony said:
Ah. I forgot to square the 2pi.

So the equation becomes:

I = mgLT^2/4pi^2

Is that correct?
Yes.
 
  • #7
alphysicist said:
That looks right to me.

Doc Al said:
Yes.

Thanks a bunch!
 
  • #8
Glad to help!
 
  • #9
Sorry for bumping up an old thread, but thought it'd be better than making a new one about the same problem. Can someone tell me where equation for I is derived from? From my knowledge I know that I = cMR^2 (as an estimated value), but what exactly do you plug into get to that point? (I = mgLT^2/4pi^2 )
 
  • #10
Hi ElTaco,

ElTaco said:
Sorry for bumping up an old thread, but thought it'd be better than making a new one about the same problem. Can someone tell me where equation for I is derived from? From my knowledge I know that I = cMR^2 (as an estimated value), but what exactly do you plug into get to that point? (I = mgLT^2/4pi^2 )

It's a standard form for the period of a physical pendulum. The derivation should be in your book, and you might also look at:

http://hyperphysics.phy-astr.gsu.edu/hbase/pendp.html
 
  • #11

What is the moment of inertia of a pendulum?

The moment of inertia of a pendulum is a measure of its resistance to changes in its rotational motion. It is a property that depends on the mass distribution and shape of the pendulum.

How is the moment of inertia of a pendulum calculated?

The moment of inertia of a pendulum can be calculated using the formula I = m*l^2, where m is the mass of the pendulum and l is the length of its arm. This assumes that the pendulum is a simple, idealized rod with all its mass concentrated at one point.

Why is the moment of inertia important in understanding the motion of a pendulum?

The moment of inertia plays a crucial role in the equations of motion for a pendulum. It determines the period of the pendulum, which is the time it takes to complete one full swing. A larger moment of inertia will result in a longer period and a slower oscillation, while a smaller moment of inertia will result in a shorter period and a faster oscillation.

How does changing the length of a pendulum affect its moment of inertia?

Changing the length of a pendulum will affect its moment of inertia, as the formula I = m*l^2 shows. A longer pendulum arm will result in a larger moment of inertia, while a shorter arm will result in a smaller moment of inertia. This means that changing the length of a pendulum will also affect its period and oscillation speed.

Does the shape of a pendulum affect its moment of inertia?

Yes, the shape of a pendulum can also affect its moment of inertia. For example, a pendulum with a wider arm will have a larger moment of inertia compared to a pendulum with a narrower arm, assuming all other factors are equal. The distribution of mass along the arm can also affect the moment of inertia. A pendulum with most of its mass concentrated at one end will have a larger moment of inertia compared to a pendulum with a more evenly distributed mass.

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