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whonut
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Homework Statement
A cylinder and pulley turn without friction about stationary horizontal axles that pass through their centres. A light rope is wrapped around the cylinder, passes over the pulley, and has a 3.00 kg box suspended from its free end. There is no slipping between the rope and the pulley surface. The uniform cylinder has mass 5.00 kg and radius 40.0 cm. The pulley is a uniform disk with mass 2.00 kg and radius 20.0 cm. The box is released from rest and descends as the rope unwraps from the cylinder. EDIT: Question is: What is the velocity of the block when it has descended 1.5m?
Homework Equations
$$\vec{\tau} = \vec{r} \times \vec{F} = I\vec{\alpha}$$
$$I = \frac{1}{2}MR^2$$
$$\alpha=\frac{a}{R}$$
The Attempt at a Solution
I have expressions for the angular accelerations of the 2 discs in terms of the tensions. ##Var_C## stands for some variable with respect to the cylinder, ##Var_B## is the same for the block and ##Var_P## is the same for the pulley.
$$\alpha_C = \frac{2T_2)}{M_{C}R_C}$$
$$\alpha_P = \frac{2(T_{1}-T_2)}{M_{P}R_P}$$
Where I get stuck is how to somehow combine those angular accelerations in order to then convert into a linear acceleration for the block. I've solved this problem by energy conservation but I really need to understand this method.
Hope I've not many faux pas, thanks in advance.
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