# Rotational equilibrium and tension question

• alimortensen
In summary, the conversation is discussing a rotational equilibrium problem involving an arm with a weight of 36.0 N. The forces of tension in the deltoid muscle and the force of the shoulder on the humerus are being determined to hold the arm in place. The sum of all torques and forces must equal zero for the system to be in equilibrium. The forces involved are gravity, the force of the shoulder, and the force of tension. Torque is calculated using the formula rFsina and the torque of the deltoid is positive while the torque of the shoulder is negative. The conversation ends with a question about the involvement of torque at the center of gravity.
alimortensen
I'm having a hard time with this rotational equilibrium problem: There is an attached image that shows the free-body diagram.

The arm in the figure weighs 36.0 N. The force of gravity acting on the arm acts through point A. Determine the magnitudes of the tension force Ft in the deltoid muscle and the force Fs of the shoulder on the humerus (upper-arm bond) to hold the arm in the position shown.

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What torques have to be balanced? How are those torques related to the forces and distances shown?

Well the entire system is in equilibrium since there is no movement. Therefore the sum of all the Torques = 0 and the sum of all the Forces =0. The forces are 1) the force of gravity going down point A (the center of gravity) 2)the Force exerted by the should on the humerus and 3) the force of tension in the deltoid muscle.

I know that Torque = rFsina
so the torque exerted by the tension in the deltoid = 0.21Ftsin168 and this is positive(?)
and the torque exerted by the force of the shoulder = 0.29Fs(sina) and this is negative (?)
Is there a torque involved in the center of gravity? I didn't think so. But that's about as far as I could get.

## 1. What is rotational equilibrium?

Rotational equilibrium is a state in which an object is not rotating or is rotating at a constant rate without any acceleration. This means that the net torque on the object is zero.

## 2. How is rotational equilibrium different from translational equilibrium?

Rotational equilibrium refers to the balance of torques on an object, while translational equilibrium refers to the balance of forces. In rotational equilibrium, the object may still be moving, but it is not accelerating due to rotation.

## 3. How is tension related to rotational equilibrium?

Tension is a force that can cause rotation, so it is an important factor in determining rotational equilibrium. If an object is suspended by a string or rope, the tension in the string must be equal to the weight of the object in order for it to be in rotational equilibrium.

## 4. What is the difference between static and dynamic equilibrium?

Static equilibrium refers to a stationary object that is not moving or rotating, while dynamic equilibrium refers to an object that is moving at a constant velocity or rotating at a constant rate. In both cases, the net force and net torque on the object are zero.

## 5. How can I calculate the tension in a string in a rotational equilibrium problem?

To calculate the tension in a string, you will need to use the equation T = rFsinθ, where T is the tension, r is the radius of the object, F is the force acting on the object, and θ is the angle between the force and the radius. You can also use the principle of torque equilibrium, where the sum of the torques on the object must be equal to zero.

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