# Torque on a pulley with a mass

• hms.tech
In summary, the conversation discusses how to calculate the torque or moment on a pulley, which is being raised by a winch. The equations for torque are given and there is some confusion about which equation is correct and why. It is determined that the torque on the pulley is due to the tension of the string, as the weight of the pulley itself does not cause torque. The conversation ends with a request for confirmation on a related problem.
hms.tech
If there is a load of say, mass =m Kg which is being raised on the end of a light inextensible rope by means of a winch.

see attachment.

the pulley of the winch has a radium x meters and is let's say that it is frictionless.
the acceleration of the load is a ms^-2

can someone tell me how would i calculate the Torque / moment on the pulley ?
i know that torque = Force * Displacement

here is what i think shud be the correct equation :

net force =N = T - mg

N[x]= Torque

But the equation in my notes says otherwise :

let K = the torque applied by the winch (the torque driving the pulley)

Torque on the pulley = K - (x)(T)

which one is correct and why ?

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hms.tech said:
can someone tell me how would i calculate the Torque / moment on the pulley ?
i know that torque = Force * Displacement

The Force here is the force applied on the pulley. From the figure you shared, what is the force on the pulley?

Sourabh N said:
The Force here is the force applied on the pulley. From the figure you shared, what is the force on the pulley?

i stated the Torque instead, and u have the radius (where the force is acting tangential)

the force on the pulley which causes it to rotate CLOCKwise = K/x

my guess is that you mean K is some other given torque.
It should be in your drawing.

Torque depends on 2 things. The force and the lever arm.
so you need to keep track of what you're torque-ing
about. in this case the natural origin is the center of
the pulley.

Torques add up - just keep track of the sign. say we pick clockwise
as positive. and calculate torque (on the pulley) about the pivot

then the net torque is the sum of
torque due to K - which is just K
torque due to m_pulley g - which is 0 (since the lever arm is 0)
torque due to T - which is -xT (x is lever arm , and minus sign is down)
so net torque is τ=K - xT

------------
also the word is should not shud, it hurts my eyes to see the latter.

qbert said:
torque due to m_pulley g - which is 0 (since the lever arm is 0)

I don't understand this point .

Would you please explain it in more detail ?

Firstly, as qbert points out, we don't see 'K' in the image, so I cannot comment on it.

Secondly, my question exactly was "From the figure you shared, what is the force on the pulley?". The figure serves as a free body diagram of the pulley, so the force on the pulley is: T, the tension acting on the rim, downwards.

Now you can use your equation: torque = Force * Displacement

To calculate the tension force: Since you know the acceleration of the block and its mass, you can calculate the tension force. This tension force is the same as the one acting at the rim of the pulley.

Sourabh N said:
This tension force is the same as the one acting at the rim of the pulley.

Why is that ?

i don't understand the free body diagram.

Why is TENSION of the string (applied on the pulley because the string is in contact with the pulley) causeing the Torque, why is weight not causing the torque ?

I see no pulley in your picture. It looks to me like a simple hoist drum lifting a load.

If you add a frictionless Lilly to the rigging then the torque on it is zero. That is the whole point of putting good bearings in a pulley.

hms.tech said:
Why is TENSION of the string (applied on the pulley because the string is in contact with the pulley) causeing the Torque, why is weight not causing the torque ?

Because the weight itself is not directly attached or connected to the pulley.

The string tension is transferred to the pulley due to friction. If there were no friction, the string would slide over the pulley and produce no torque.

Because we are calculating torque about the center of mass of the pulley and weight of the pulley is acting at the center of mass.

There is no torque at a point due to a force at the same point. Do you know why?

EDIT: Above post answers why weight of the block is not causing torque, this post answers why weight of pulley isn't causing torque.

Sourabh N said:
There is no torque at a point due to a force at the same point. Do you know why?

Because the weight of the pulley acts downwards passing through the axis of rotation, thus the Torque = W*r

W = weight of pulley
r= zero

Right, so weight is not causing the torque. Tension is applied at the rim of the pulley, it's not passing through the axis of rotation, so it does have a torque.

Another related problem for me [here]

## 1. What is torque on a pulley with a mass?

Torque is a measure of the rotational force applied to an object. In the case of a pulley with a mass, it refers to the force applied to the pulley due to the weight of the mass attached to it.

## 2. How is torque calculated on a pulley with a mass?

To calculate the torque on a pulley with a mass, you need to multiply the force applied to the pulley (in this case, the weight of the mass) by the distance from the point of rotation to where the force is applied.

## 3. What factors affect the torque on a pulley with a mass?

The factors that affect torque on a pulley with a mass include the mass of the object attached to the pulley, the force applied to the pulley, and the distance from the point of rotation to where the force is applied.

## 4. How does the direction of the force affect the torque on a pulley with a mass?

The direction of the force applied to the pulley affects the direction of the torque. If the force is applied in the same direction as the rotation of the pulley, it will increase the torque. If the force is applied in the opposite direction, it will decrease the torque.

## 5. What is the relationship between torque and rotational acceleration on a pulley with a mass?

The relationship between torque and rotational acceleration on a pulley with a mass is directly proportional. This means that an increase in torque will result in an increase in rotational acceleration, and a decrease in torque will result in a decrease in rotational acceleration.

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