# Finding the tension in a pulley that rotates

• PhyIsOhSoHard
In summary, the problem involves finding the tensions (T_1, T_2, T_3) when m_2 is greater than m_1 and the pulley is rotating. Newton's laws can be used to solve the problem, but the system will have a net acceleration due to the rotation of the pulley.
PhyIsOhSoHard

## Homework Statement

$m_2>m_1$
The pulley rotates.
Find the tensions, $T_1, T_2, T_3$

Newton's laws

## The Attempt at a Solution

I know how to solve the problem if the pulley doesn't rotate because the systems would be in equilibrium (Newton's first law) and dividing into 3 systems (one for each tension) you get $T_1=m_1g$, $T_2=m_2g$ and $T_3=m_1g+m_2g$.

But I have no idea what changes when the pulley starts rotating. Can somebody give me some leads?

Well if the pulley starts rotating it will do so in such a way so that m2 will start falling because it is more massive. The only difference here is that when you do Newtons Second Law on the system, there will be a net acceleration.

## 1. How do you calculate the tension in a pulley that rotates?

The tension in a pulley that rotates can be calculated using the formula T = (M1 x R1) + (M2 x R2), where T is the tension, M1 and M2 are the masses of the objects on either side of the pulley, and R1 and R2 are the radii of the pulley on each side.

## 2. What factors affect the tension in a rotating pulley?

The tension in a rotating pulley is affected by the masses of the objects on either side of the pulley, the radii of the pulley on each side, and the acceleration of the objects. Friction and the angle of the rope or belt on the pulley can also impact the tension.

## 3. How does the direction of rotation affect the tension in a pulley?

The direction of rotation does not have a direct impact on the tension in a pulley. However, if the direction of rotation changes, it could potentially change the direction of the forces acting on the pulley, which could then affect the tension.

## 4. What is the difference between static and dynamic tension in a rotating pulley?

Static tension refers to the tension in a pulley when the objects on either side are not moving. Dynamic tension, on the other hand, refers to the tension when the objects are in motion. In a rotating pulley, the dynamic tension may be greater than the static tension due to the added forces of acceleration and friction.

## 5. How can the tension in a rotating pulley be measured?

The tension in a rotating pulley can be measured using a spring scale or a force sensor. The scale or sensor should be attached to the rope or belt on one side of the pulley, and the tension can be read from the scale or sensor in units of force (such as Newtons or pounds).

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