# Torque & Equilibrium: Translational & Rotational

• asdasdasd
In summary, the conversation discusses a problem given in class that involves finding the values of T, T_2y, T_3y, and T_3x in a system that is in translational and rotational equilibrium. The equations used to solve the problem are listed, and the proposed values for each variable are also given. The speaker asks for confirmation on whether their solution is correct.
asdasdasd
Torque/Translational and Rotational Equilibrium

I was given this problem as a quiz in class. Unfortunately, I did not finish it. I decided to try it at home as I need the practice.

## Homework Statement

Sorry for the crudely drawn image.
http://image.bayimg.com/lajgkaabb.jpg

Find: $$T, T_2y, T_3y, T_3x$$ given $$T_2y = T_3y$$ and the object is in translational and rotational equilibrium.

Figure of problem also attached.

## Homework Equations

Don't think there are any.

## The Attempt at a Solution

Sum of all forces is zero.

$$\Sigma x = T_3x + -T\cos30^\circ = 0$$
$$\Sigma y = 2T_2y + T\sin30^\circ - 500N = 0$$

Sum of torque is zero.

$$\Sigma\Gamma = -(4m)(2T_2y) + (1.75m)T_3x + (2m)(500N)$$

Substitution time?

$$T_3x = T\cos30^\circ$$
$$T_2y = \frac{500N - T\sin30^\circ}{2}$$
$$0N = -(4m)(500N - T\sin30^\circ) + (1.75m)(T\cos30^\circ) + 1000N$$
$$0N = -1000N + 3.516T$$

Proposed values

$$T = 284.414N$$
$$T_3x = 246.31N$$
$$T_2y = T_3y = 178.896N$$

I just want to know if I did this correctly. If not, I would greatly appreciated any help. Thanks for taking the time to read this.

#### Attachments

• hajgfaabb.png
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Sorry to bump my own thread... I just want to know if I did the problem correctly...

Hello,

I can confirm that your approach to this problem is correct. You correctly identified the equations needed to solve for the unknown tensions and used substitution to solve for them. Your proposed values for T, T_3x, T_2y, and T_3y are also correct. Overall, you have successfully demonstrated an understanding of torque, equilibrium, and how to apply them to solve a problem. Great job! Keep practicing and you will continue to improve your skills in this area.

## 1. What is torque?

Torque is a measure of the force that causes an object to rotate around an axis. It is calculated by multiplying the force applied to an object by the distance from the axis of rotation.

## 2. How does torque affect rotational equilibrium?

In order for an object to be in rotational equilibrium, the net torque acting on it must be zero. This means that all the clockwise and counterclockwise torques must balance out, resulting in no rotation.

## 3. What is the difference between translational and rotational equilibrium?

Translational equilibrium refers to a state where an object is not accelerating or moving in a straight line, while rotational equilibrium refers to a state where an object is not rotating. Both types of equilibrium require a balance of forces or torques.

## 4. How do you calculate the center of mass for an object?

The center of mass for an object can be calculated by finding the weighted average of all the individual masses in the object, taking into account their distances from a reference point. It is the point where all the mass of an object can be considered to be concentrated.

## 5. What factors affect an object's stability in rotational equilibrium?

An object's stability in rotational equilibrium is affected by its shape, mass distribution, and the location of its center of mass. Objects with a wider base and a lower center of mass are generally more stable in rotational equilibrium.

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