- #1
lukast
- 1
- 0
Homework Statement
The system looks like this:
I have two discs which are connected.
Disc 1 has ##R_1##(radius) and ##M_1##(mass)
Disc 2 has ##R_2## and ##M_2##
## R_2 > R_1 ##
## M_2 > M_1 ##
on both discs weights are attached on opposite sides.
On smaller ##m_1## is pulling and on bigger ##m_2##
##m_2 > m_1##
i need to calculate angular acceleration and accelerations of both weights
Homework Equations
[/B]
## F = m * a ##
## \alpha = \frac{a}{R} ##
## M = I * \alpha ##
## Q = m * g ##
The Attempt at a Solution
The force that would cause acceleration of system is equal to :
## F = Q_2 - Q_1 ##
## F = m_2*g - m_1*g ##
The force that will cause tangential acceleration of discs would be equal to :
## I * \alpha = M ##
## \frac{1}{2} m * R^2 * \frac{a}{R} = F * R ##
## \frac{1}{2}*m * a = F ##
Now we know that Disc 2 and ##m_2## will have the same accelerations and Disc 1 and ##m_1## will have the same accelerations. We also now that Disc 1 and Disc 2 also have same angular acceleration. So from that i thought i can write this:
## a_1*(\frac{1}{2} * M_1 + m_1) + a_2(\frac{1}{2}*M_2 + m_2) = F ## (force that cause acceleration)
## a = \alpha * R##
##\alpha * R_1 *(\frac{1}{2} * M_1 + m_1) + \alpha * R_2 *(\frac{1}{2}*M_2 + m_2) = F##
and i have everything to get an alpha but its wrong
if somebody solve this on different way, could please explain why is my approach wrong[/B]
Last edited: