Question

In this system, how can you determine which direction it will rotate?

Answer 1

Like, if \(m_1\) is larger than \(m_2\), how can you tell which way it will rotate?

Answer 2

Sorry for keeping asking you for help, but can you answer this question, @shubhamsrg ?

Answer 3

Product of mr will decide that

Answer 4

Why does it work?

Answer 5

Clockwise torque = (m2)g(r2)
ANti clockwise torque = (m1)g(r1)

Greater torque will prevail

Answer 6

I'm confused...

Answer 7

Also, am assuming its a massless pulley , right ?

Answer 8

Well, the problem I'm currently working on, it doesn't say anything about the mass of pulley... but it does say that the combined moment of inertia of the two wheels is 2.7 kg·m².

So pulley or wheels has mass?

Answer 9

Yes pulleys has mass.

Answer 10

Here's the problem.

Answer 11

Be right back.

Answer 12

The reason I ask this question is because I want to set up a sum of force for both two masses correctly and I don't know which to go first; mg or T (tension)

Answer 13

If mass goes upward, T goes first, otherwise, m·g goes first.

Answer 14

My attempt is to set up some equations then do some substitution and isolate and find \(\alpha\) in term of variables that already have given value. I don't know if this can work.

Answer 15

Okay am back

Answer 16

Well simply write eqn of rotation.

Answer 17

\(\sum \tau = T_1R_1 - T_2 R_2 = I\alpha\) OR \(\sum \tau = T_2R_2 - T_1 R_1 = I\alpha\) It depends which direction it rotates... I also need to find two tensions...

Answer 18

\[\sum F_1 = m_1g - T_1 = m_1 a\] OR \[\sum F_1 = T_1 - m_1g = m_1 a\]

\[\sum F_2 = m_2g - T_2 = m_2 a\] OR \[\sum F_2 = T_2 - m_2g = m_2 a\]

That's why I need to determine which direction it rotates...

Answer 19

Any ideas?

"Clockwise torque = (m2)g(r2)
ANti clockwise torque = (m1)g(r1)

Greater torque will prevail"

This works only if pulley is massless, right?

Answer 20

You can take any direction to be +ve. If your assumption would be wrong, it'll automatically come to be -ve

Answer 21

Ugh, I hope I make right guess first, lol.

Answer 22

What is ve?

Answer 23

negatiVE

Answer 24

What is angular acceleration is negative? How can I know if my assumption is right or wrong?

Answer 25

Problem asks me to "take clockwise direction as positive."

Answer 26

Wait, angular acceleration cannot be negative, right?

Answer 27

It is a vector, it can be negavtive, -ve will just denote the direction.

Answer 28

The linear acceleration of both masses will not be equal

Answer 29

m1g - T1 = m1 a1

T2 - m2g = m2 a2

T1 r1 - T2 r2 = I alpha

Answer 30

Is it possible to find angular acceleration in this way?

Answer 31

I am getting confused.
@Vincent-Lyon.Fr

Answer 32

It seems like there is too much unknown variables.

Answer 33

lol, me too...

Answer 34

@hartnn @JamesJ @saifoo.khan Can you help me?

Answer 35

@zepdrix @AccessDenied

Answer 36

Apparently I'm not going to get any help for long time.

Answer 37

You don't have to know the direction of rotation of the pulley before you solve the equations.
You just take one of the directions as positive and the other one as negative. This choice is completely arbitrary (But since the given problem asks you to take the clockwise direction as positive, you just go ahead with that).
After you solve the problem, if the end up with positive angular acceleration, it's in the direction that you chose (In this case, clockwise). If it turns out to be negative, it's in the opposite direction (In this case, counter-clockwise).

Answer 38

Quote :
"Clockwise torque = (m2)g(r2) ANti clockwise torque = (m1)g(r1) Greater torque will prevail" This works only if pulley is massless, right?


No, this works whatever the moment of inertia of the pulley.
It is a good idea to anticipate the direction of motion this way.

Answer 39

It makes sense. Thanks, everybody!