- #1
Dazed&Confused
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Homework Statement
A disk rotates with constant angular velocity [itex]\omega[/itex]. Two masses, [itex]m_A[/itex] and [itex]m_B[/itex], slide without friction in a groove passing through the centre of the disk. They are connected by a light string of length [itex]l[/itex], and are initially held in position by a catch, with mass [itex]m_a[/itex] at a distance [itex]r_A[/itex] from the centre. Neglect gravity. At [itex]t=0[/itex] the catch is removed and the masses are free to slide. Find [itex]\ddot{r_A}[/itex] immediately after the catch is removed in terms of [itex]m_A, m_B, l, r_A,[/itex] and [itex]\omega[/itex]
The Attempt at a Solution
Since the string is light, the tension on each side is equal.
We have [itex]T = m_A\omega^2r_A - m_A\ddot{r_A} = m_B\omega^2(l-r_A) - m_B\ddot{r_B}[/itex]. If I had another equation in terms of [itex]\ddot{r_A}[/itex] and [itex]\ddot{r_B}[/itex] then I could solve for [itex]\ddot{r_A}[/itex]. There is an angular acceleration of magnitude [itex]2\omega\dot{r_A}[/itex] but I don't know how to use this. Any help with this would be appreciated.