# Problem with the weigth of the moment arm

• SwedishFred
In summary, the conversation discusses a rod with a counterweight, handle, and hook that hangs a mass of 400g. The rod is 0.8m long and equilibrium is achieved when the handle is at a position X = 12.0cm. The individual calculates the length of the handle and the total mass of (m) to obtain equilibrium. One person suggests using calculus to find the total moment, while the other suggests finding the mass center of the rod without calculus. Eventually, they determine that the mass center is at 0.28m and the total mass of (m) is 0.112kg.
SwedishFred
Hi
A rod comprises a counterweight (a) a handle and a hook which hangs mass (m), the rods mass is 400g counterweight mass (a) = 1600g and the rod is 0.8m long. Equilibrium exists when the handle is at position X = 12.0cm

How I did

1: calculated the length of the handle to (m) which was 0.68m
2: figured kg from 1.6 kg * 0.12 = 0.192 kg
3 0.192 = 0.68*m
but how do you do with the rod weighs 400g how do I calculate it??
The question is to calculate the total mass of (m) to obtain equilibrium
hope you understand the language and metrics, used google translate, did work out that great, but I´m loosing time

regards fredrik

Consider a uniform horizontal rod length L pivoted at one end. Using calculus:
An element length dx at distance x from the pivot has mass ρdx. What is its moment about the pivot? Can you integrate that to get the total moment?
Or, without calculus, where is the mass centre of the rod?

Oki now I see, its in its center then You just calculated it to the handle..
0.8/2-0.12=0.28
0.4kg*0.28=0.112kg

Thanx for your help! Sent from my iPhone using Physics Forums

## 1. What is the moment arm and why is it important?

The moment arm is the shortest distance between the point of rotation and the line of action of a force. It is important because it determines the amount of torque or rotational force that is produced by a force applied to an object.

## 2. What causes a problem with the weight of the moment arm?

A problem with the weight of the moment arm typically occurs when the moment arm is not perpendicular to the direction of the applied force. This causes the force to have a component that is parallel to the moment arm, resulting in a decreased torque.

## 3. How does the weight of the moment arm affect the stability of an object?

The weight of the moment arm affects the stability of an object by increasing or decreasing its ability to resist rotational forces. A longer moment arm can provide greater stability, while a shorter moment arm can make an object more prone to tipping over.

## 4. Can the weight of the moment arm be adjusted?

Yes, the weight of the moment arm can be adjusted by changing the distance between the point of rotation and the line of action of the force. This can be done by changing the position of the force or the point of rotation.

## 5. How does the weight of the moment arm impact everyday objects and activities?

The weight of the moment arm impacts everyday objects and activities by affecting their stability, strength, and ease of use. For example, a ladder with a longer moment arm is more stable and can support more weight, while a shorter moment arm can make opening a door more difficult.

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