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Like, if \(m_1\) is larger than \(m_2\), how can you tell which way it will rotate?
Product of mr will decide that
Why does it work?
Clockwise torque = (m2)g(r2) ANti clockwise torque = (m1)g(r1) Greater torque will prevail
Also, am assuming its a massless pulley , right ?
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?
Yes pulleys has mass.
Be right back.
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)
If mass goes upward, T goes first, otherwise, m·g goes first.
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.
Okay am back
Well simply write eqn of rotation.
\(\sum \tau = T_1R_1 - T_2 R_2 = I\alpha\) 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...
\[\sum F_1 = m_1g - T_1 = m_1 a\] 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...
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?
You can take any direction to be +ve. If your assumption would be wrong, it'll automatically come to be -ve
Ugh, I hope I make right guess first, lol.
What is ve?
What is angular acceleration is negative? How can I know if my assumption is right or wrong?
Problem asks me to "take clockwise direction as positive."
Wait, angular acceleration cannot be negative, right?
It is a vector, it can be negavtive, -ve will just denote the direction.
The linear acceleration of both masses will not be equal
m1g - T1 = m1 a1 T2 - m2g = m2 a2 T1 r1 - T2 r2 = I alpha
Is it possible to find angular acceleration in this way?
It seems like there is too much unknown variables.
lol, me too...
Apparently I'm not going to get any help for long time.
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).
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.
It makes sense. Thanks, everybody!