Calculating the A value of a physical pendulum

In summary, the equation for the moment of inertia of an arm or leg can be expressed as I = AmL^2, where A is a unitless number that depends on the axis of rotation and the geometry of the limb and L is the distance from the center of mass. For a person with arms that are 31.30 cm in length and legs that are 40.69 cm in length, the value of A is 1.142.
  • #1
ttk3
28
0

Homework Statement



The moment of inertia for an arm or leg can be expressed as I = AmL^2, where A is a unitless number that depends on the axis of rotation and the geometry of the limb and L is the distance from the center of mass. Say that a person has arms that are 31.30 cm in length and legs that are 40.69 cm in length and that both sets of limbs swing with a period of 1.20 s. Assume that the mass is distributed uniformly in both the arms and legs.

Calculate the value of A for the person's arms.


L arm = .313 m
T = 1.20

Homework Equations



A = (g/L) (T/2pi)^2

The Attempt at a Solution




(9.8/.313) (1.20/2pi)^2 = 1.142

I'm not sure where I'm going wrong with this problem. After the derivation of the equation it's plug and chug. I looked up the equation I derived and it's correct. Can anyone lend me a hand?
 
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  • #2
Hi ttk3,

What does L represent in the equation? You plugged in the length of the arm but I don't think that's correct.
 
  • #3
It says that L is the distance from the center of mass. Wouldn't the center of mass be located at the top of the arm (the point from which the pendulum swings)?

The equation is derived from the attached equation, and L would be the arm length in that one I thought.
 

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  • #4
ttk3 said:
It says that L is the distance from the center of mass. Wouldn't the center of mass be located at the top of the arm (the point from which the pendulum swings)?

The equation is derived from the attached equation, and L would be the arm length in that one I thought.

I can't view the attachment yet, but the center of mass would not be at the top of the arm. The problem indicates that the mass is uniformly distributed in the arm.

Pretend the arm is a uniform rod. Where is the rod's center of mass? It's not at either end of the rod.

Also, when you say that L is the distance from the center of mass, is that all it said? That does not sound like it is complete. Shouldn't it be something like, L is the distance from the center of mass to the shoulder (arm's pivot point)? Because distances are between two points.
 
  • #5
The question is a direct copy and paste from the program. So if the center of mass is the center of the arm, would I the length of the arm divided by two for my L value?
 
  • #6
If L is the distance from the center of mass to the shoulder, then that sounds right to me. What do you get?
 

Related to Calculating the A value of a physical pendulum

1. How do you calculate the A value of a physical pendulum?

The A value of a physical pendulum can be calculated by using the formula A = (mgd)/I, where m is the mass of the pendulum, g is the acceleration due to gravity, d is the distance from the pivot point to the center of mass, and I is the moment of inertia of the pendulum.

2. What is the moment of inertia for a physical pendulum?

The moment of inertia for a physical pendulum is a measure of its resistance to rotational motion and is calculated using the formula I = md^2, where m is the mass of the pendulum and d is the distance from the pivot point to the center of mass.

3. Can the A value be negative for a physical pendulum?

Yes, the A value can be negative for a physical pendulum if the distance d is measured in the opposite direction of the gravitational force. This indicates that the pendulum is unstable and will not oscillate in a regular manner.

4. How does changing the mass affect the A value for a physical pendulum?

Changing the mass of the pendulum will directly affect the A value, as it is a factor in the calculation. Increasing the mass will result in a larger A value, while decreasing the mass will result in a smaller A value.

5. What factors can affect the accuracy of the A value calculation for a physical pendulum?

The accuracy of the A value calculation for a physical pendulum can be affected by factors such as the precision of the measurements taken for mass, distance, and time, as well as external factors like air resistance or friction at the pivot point. It is important to minimize these sources of error to get an accurate A value.

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