- #1
Karol
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Homework Statement
A rod of length l swivels around an axis, denoted O in the drawing, located on the floor.
The initial position is β=45°.
A ball B is left to fall at the same time the rod is left to rotate.
Who will arrive, first, to the floor: the ball or the edge A of the rod
Homework Equations
T(torque)=Iα
Moment of inertia of the rod around it's edge:
[tex]I_o=\frac{1}{3}ml^2[/tex]
The Attempt at a Solution
The torque at different angles α:
[tex]\frac{l}{2}mg\cdot \cos \beta=\frac{1}{3}ml^2 \cdot \alpha[/tex]
And the geometric relation:
[tex]l \cdot \alpha=a_A[/tex]
Where aA is the acceleration of the edge of the rod.
[tex]\rightarrow a_A=\frac{3lg\cdot \cos \beta}{2}[/tex]
I integrate aA in the range of β=45° to β=0° and get a number for the velocity of the edge of the rod A at the floor, but i cannot integrate further this velocity in order to make it equal to the length of the arc and extract the time.