geerky42 2 years ago In this system, how can you determine which direction it will rotate?

1. geerky42

2. geerky42

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

3. geerky42

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

4. shubhamsrg

Product of mr will decide that

5. geerky42

Why does it work?

6. shubhamsrg

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

7. geerky42

I'm confused...

8. shubhamsrg

Also, am assuming its a massless pulley , right ?

9. geerky42

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?

10. shubhamsrg

Yes pulleys has mass.

11. geerky42

Here's the problem.

12. shubhamsrg

Be right back.

13. geerky42

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)

14. geerky42

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

15. geerky42

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.

16. shubhamsrg

Okay am back

17. shubhamsrg

Well simply write eqn of rotation.

18. geerky42

$$\sum \tau = T_1R_1 - T_2 R_2 = I\alpha$$ 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...

19. geerky42

$\sum F_1 = m_1g - T_1 = m_1 a$ 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...

20. geerky42

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?

21. shubhamsrg

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

22. geerky42

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

23. geerky42

What is ve?

24. shubhamsrg

negatiVE

25. geerky42

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

26. geerky42

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

27. geerky42

Wait, angular acceleration cannot be negative, right?

28. shubhamsrg

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

29. shubhamsrg

The linear acceleration of both masses will not be equal

30. shubhamsrg

m1g - T1 = m1 a1 T2 - m2g = m2 a2 T1 r1 - T2 r2 = I alpha

31. geerky42

Is it possible to find angular acceleration in this way?

32. shubhamsrg

I am getting confused. @Vincent-Lyon.Fr

33. geerky42

It seems like there is too much unknown variables.

34. geerky42

lol, me too...

35. geerky42

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

36. geerky42

@zepdrix @AccessDenied

37. geerky42

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

38. rajathsbhat

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).

39. Vincent-Lyon.Fr

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.

40. geerky42

It makes sense. Thanks, everybody!