Calculate A for Person's Arms in Oscillatory Motion

In summary, the moment of inertia for an arm or leg is expressed as I = amL2 and depends on the axis of rotation, geometry of the limb, and distance to the center of mass. For a person with arms of 27.80 cm and legs of 38.92 cm, both swinging with a period of 1.40 s, the value of A for the arms can be calculated using the equation T = 2π√(I/mgL). However, the given information is not enough to determine the value of A. The equation can still be used to solve for I, but the mass (m) is unknown. Further clarification or additional information is needed to solve for A.
  • #1
sheri1987
48
0

Homework Statement



The moment of inertia for an arm or leg can be expressed as I = amL2, where a is a unitless number that depends on the axis of rotation and the geometry of the limb and L is the distance to the center of mass. Say that a person has arms that are 27.80 cm in length and legs that are 38.92 cm in length and that both sets of limbs swing with a period of 1.40 s. Assume that the mass is distributed evenly over the length for both the arm and leg.

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



Homework Equations



I am not sure of any equations that include Amplitude.

Here is one that relates to the problem, but cannot be used to solve A:

T = 2pi(sqrt(I/mgL))


T= period given (1.4 s)
I = ?
L = given 27.80
g = gravity 9.81
m =?

The Attempt at a Solution



I'm just really confused on how to go about this problem? Any advice?
 
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  • #2
Are you sure its amplitude they want and not the little constant in the moment of inertia equation?
 
  • #3


I understand your confusion with this problem. The given equation is not sufficient to solve for A, as it does not include any information about amplitude. However, we can use the given information about period and length to calculate the moment of inertia (I) for the arms.

Using the given equation for moment of inertia (I = amL2) and assuming that the mass is evenly distributed over the length of the arm, we can rewrite the equation as I = m(L2/a).

To solve for I, we need to determine the mass (m) and the value of a. We can use the given information about the period and length to calculate the value of a.

First, we need to determine the angular frequency (ω) using the given period (T) and the equation ω = 2π/T. Plugging in the values, we get ω = 2π/1.4 s = 4.48 rad/s.

Next, we can use the equation T = 2π/ω to solve for the value of a. Plugging in the values, we get 1.4 s = 2π/(4.48 rad/s * L/a). Solving for a, we get a = 2πL/T = 2π(0.278 m)/1.4 s = 1.256 m^-1.

Now, we can plug in the values for mass (m = 1 kg) and the calculated value for a (a = 1.256 m^-1) into the equation for moment of inertia to solve for I.

I = m(L2/a) = (1 kg)(0.278 m)2/(1.256 m^-1) = 0.623 kgm^2.

Therefore, the value of A for the person's arms in oscillatory motion would be A = √(I/mgL) = √(0.623 kgm^2/(1 kg * 9.81 m/s^2 * 0.278 m)) = 0.887 m.

I hope this helps to clarify the solution for this problem. It is important to carefully analyze the given information and use appropriate equations to solve for the desired value.
 

1. What is the formula for calculating A for a person's arms in oscillatory motion?

The formula for calculating A (amplitude) for a person's arms in oscillatory motion is A = (maximum distance reached by arm) - (resting position of arm).

2. How do you measure the maximum distance reached by a person's arm in oscillatory motion?

The maximum distance reached by a person's arm in oscillatory motion can be measured using a ruler or tape measure. The person's arm should be fully extended in the direction of motion and the distance from the resting position to the furthest point reached should be measured.

3. Can A be negative in oscillatory motion?

No, A (amplitude) cannot be negative in oscillatory motion. It represents the maximum displacement from the resting position, so it is always a positive value.

4. How does the mass of a person's arm affect the value of A in oscillatory motion?

The mass of a person's arm does not directly affect the value of A (amplitude) in oscillatory motion. However, a heavier arm may require more force to reach a certain amplitude, so it may indirectly affect the motion.

5. Is there a relationship between A and the frequency of oscillatory motion for a person's arms?

Yes, there is a relationship between A (amplitude) and the frequency of oscillatory motion for a person's arms. As the amplitude increases, the frequency will decrease, and vice versa. This relationship is described by the equation A = (2π/ω) * v, where ω is the angular frequency and v is the linear velocity of the arm.

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