Moment of Inertia/Torque - Calculating the Angular Velocity of a Catapult Arm

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In summary, the conversation discusses the calculation of torque and moment of inertia for a catapult project. The user has solved for torque but has doubts about the moment of inertia and asks for confirmation. They also ask about the center of mass of the arm and whether the other masses involved affect it. The expert advises to find the center of mass by seeing where the arm balances and to not worry about the other masses when calculating the arm's center of mass.
  • #1
JJX
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Hi all, I'm working on a catapult for a project and I'm having some problems with some of the calculations, I'm trying to get the angular velocity of my catapult's arm by first obtaining the torque and moment of inertia.

Homework Statement


http://img46.imageshack.us/img46/2687/physproblem.th.png
A diagram I made with all the information and the sum of torques solved.

Homework Equations


Torque = Force * Distance to axis of rotation
I=(1/12)ML^2 + MD^2
F = mg

3.Attempt at solution
I've solved Torque, but I have some doubts for Moment of Inertia:
1) Is M the mass of the arm by itself or the addition of all the masses involved (arm+counterweight+basket+projectile)
2) Is L the distance of the whole Arm and D the distance of the axis of rotation to the center of mass?

I=(1/12)ML^2 + MD^2
I=(1/12)(0.9)(.3650)^2 + (0.9)(.1)^2
I=.0189 kg*m^2
Is this right?
 
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  • #2
Can anyone at least confirm that my solution is right?
 
  • #3
First, welcome to Physics Forums :smile:
JJX said:
A diagram I made with all the information and the sum of torques solved.
Since the axis of rotation is not at the arm's center of mass, you need to add a torque term for the arm.

Homework Equations


Torque = Force * Distance to axis of rotation
I=(1/12)ML^2 + MD^2
F = mg

3.Attempt at solution
I've solved Torque, but I have some doubts for Moment of Inertia:
1) Is M the mass of the arm by itself or the addition of all the masses involved (arm+counterweight+basket+projectile)
2) Is L the distance of the whole Arm and D the distance of the axis of rotation to the center of mass?

I=(1/12)ML^2 + MD^2
I=(1/12)(0.9)(.3650)^2 + (0.9)(.1)^2
I=.0189 kg*m^2
Is this right?
1) M is just the arm mass
2) Yes to both
HOWEVER ... this I is the M.O.I. for the arm only. You need to add the contributions of the projectile+basket and counterweight, to get I for the entire catapult. These would be m·d2 for each mass, using the distance from the axis of rotation.
 
  • #4
Thank You Red Belly, that was extremely helpful. I have now come across another problem, I need to find the centre of mass of this very same arm. Is it always the centre? I placed it there by the way, seemed right. Does it have anything to do with the Masses*r aswell? I wonder if the counterweight and the basket affect it.
 
  • #5
You can find the center of mass for yourself by seeing where the arm balances.

Is the arm thicker or heavier at one end? If not, and it is a uniform cross-section size along it's whole length, then the center of mass should be in the middle of the arm. If you can verify this by checking where the balance point is (with no other masses attached), all the better.

Don't worry about the other masses when calculating the arm's center of mass. You are accounting separately for those masses' contribution to torque and moment of inertia.
 

FAQ: Moment of Inertia/Torque - Calculating the Angular Velocity of a Catapult Arm

What is moment of inertia?

Moment of inertia is a measure of an object's resistance to changes in rotational motion. It is the sum of the product of an object's mass and the square of its distance from the axis of rotation.

How is moment of inertia calculated?

The moment of inertia of a point mass is equal to the mass times the square of the distance from the axis of rotation. For a continuous object, it can be calculated by integrating the mass distribution over the object's volume or surface.

What is torque?

Torque is the measure of a force's effectiveness at causing rotation. It is calculated by multiplying the force applied by the perpendicular distance from the axis of rotation to the point where the force is applied.

How are moment of inertia and torque related?

Moment of inertia and torque are related in that they both affect an object's rotational motion. Torque is the result of a force acting on an object, while moment of inertia is the object's resistance to changes in rotational motion. The larger the moment of inertia, the greater the torque required to change the object's rotational motion.

What are some real-world applications of moment of inertia and torque?

Moment of inertia and torque have practical applications in various fields, including engineering, physics, and sports. For example, moment of inertia is important in designing cars and airplanes to ensure stability and control. Torque is used in calculating the power output of engines and motors, and in determining the force required to loosen or tighten bolts. In sports, moment of inertia is an important factor in determining the performance of equipment such as golf clubs and tennis rackets, while torque is essential in activities such as weightlifting and rowing.

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