Why are the forces on torque tension and not the weight of the mass?

[j04015]

Homework Statement

Check image attached
I have a hard time understanding why the F in T=FR is tension and not the weight of the blocks

Isn't weight the force that's making the disk rotate? I thought tension was just an opposing force.

Relevant Equations

T=Iα

Let the left string be T1 and the right string be T2. Pretend that the masses are NOT equal and that the total mass on the left is 3mg and the total mass on the right is 2mg.

My first thought: Net torque = 3mgR1-2mgR1

Actual solution: Net torque = (T1-T2)*R

Once again, the force that's used is tension and not the weight of the mass (which I'm assuming is what makes the system move). I just need some advice on understanding why that's the case.

 

[PeroK]

Homework Statement: Check image attached
I have a hard time understanding why the F in T=FR is tension and not the weight of the blocks

Isn't weight the force that's making the disk rotate? I thought tension was just an opposing force.
Relevant Equations: T=Iα

View attachment 337044
Let the left string be T1 and the right string be T2. Pretend that the masses are NOT equal and that the total mass on the left is 3mg and the total mass on the right is 2mg.

My first thought: Net torque = 3mgR1-2mgR1

That's not a bad first thought. But, are you sure it's your final answer?

Actual solution: Net torque = (T1-T2)*R

That must be true, because only the string is attached to the wheel.

Once again, the force that's used is tension and not the weight of the mass (which I'm assuming is what makes the system move). I just need some advice on understanding why that's the case.

The mass difference is the cause of the motion, but you need to make sure that all the relevant equations are satisfied. For example, if ##T_1 = 3mg##, what does Newton's second law say about the motion of the ##3m## mass?

 

[hutchphd]

Homework Statement: Check image attached
I have a hard time understanding why the F in T=FR is tension and not the weight of the blocks

Isn't weight the force that's making the disk rotate? I thought tension was just an opposing force.
Relevant Equations: T=Iα

Once again, the force that's used is tension and not the weight of the mass (which I'm assuming is what makes the system move). I just need some advice on understanding why that's the case.

Your first guess tacitly assumes that the system is static and that will lead to the incorrect answer. Slow and steady solves the problem.

 

[kuruman]

Your first guess tacitly assumes that the system is static and that will lead to the incorrect answer.

Not quite right. If the net torque is τ_net = 3mgR1 - 2mgR1, the system cannot be static because the net torque is not zero. The system is static if it is at rest and remains at rest. This value of τ_net is the initial value of the net torque at the moment of release before the string stretches a bit when the angular velocity is zero and the angular acceleration is ##\alpha = \tau_{\text{net}}/I.##

 

[hutchphd]

My statement was perhaps too nuanced. His (tacit) intuition about tension was, I believe, predicated upon this misapprehension somewhere in his chain of thought (trying to work it out in his head). A common source of error for people used to intuiting the answers without recourse to their ongoing education

 

[Steve4Physics]

Once again, the force that's used is tension and not the weight of the mass (which I'm assuming is what makes the system move). I just need some advice on understanding why that's the case.

Try this. A block has mass =2kg and hangs from a string. Take g=10N/kg.
What is the tension when:
a) the block's acceleration is zero?
b) the block's acceleration is 3m/s² upwards?
c) the block's acceleration is 3m/s² downwards?

The forces directly acting on the wheel are the tensions. So in a non-equilibrium (unequal hanging masses) situation, you must use the values of the tensions, not the values of the weights.

Minor edits.

 

[haruspex]

Not quite right. If the net torque is τ_net = 3mgR1 - 2mgR1, the system cannot be static because the net torque is not zero. The system is static if it is at rest and remains at rest. This value of τ_net is the initial value of the net torque at the moment of release before the string stretches a bit when the angular velocity is zero and the angular acceleration is ##\alpha = \tau_{\text{net}}/I.##

I assumed @hutchphd meant held static.

why the F in T=FR is tension and not the weight of the blocks

This is a common error.
The disc is an inanimate object. Unlike you, it cannot see the source of the tension. It can only react to those forces that act directly on it.
Since the masses will move, there is a net force on them. Consequently their weights cannot equal the tension.

 

[kuruman]

My statement was perhaps too nuanced. His (tacit) intuition about tension was, I believe, predicated upon this misapprehension somewhere in his chain of thought (trying to work it out in his head). A common source of error for people used to intuiting the answers without recourse to their ongoing education

I agree. I posted for the record.

I assumed @hutchphd meant held static.

I thought about that, but I wasn't sure. After all, if the system is held static there must be a third entity, in addition to the two weights, holding it static.