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The kinetic energy possessed by the weight depends on its mass (given) and its velocity. The rotational kinetic energy of the cylinder depends on its moment of inertia (found from given information) and its angular velocity. But, because of the cable, the angular velocity of the cylinder is related to the linear velocity of the block, through the radius ...

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What is angular speed? Clearly it is $\frac {v_\perp} {r}$ where symbols have their usual meanings. Rod rotates about its, say, rightmost point, say $O$. We will consider left side as positive $x$-axis. Now consider a point $A$ at distance $r_1$ from it. Let the rod have instantaneous angular speed $\omega$. All points on the rod will have this $\omega$ ...

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Let's try to apply Newtonian mechanics to this problem. Since the ball is initially at rest, determining the resulting direction of motion, if any, boils down to determining the direction of the net force on the ball as it spins. If the direction of the net force isn't obvious (like it might not be here), try teasing out some force by focusing on a ...

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