Question

3. A 75 g, 30 cm long rod hangs vertically on a friction less, horizontal axel passing through the center. A 10 g ball of clay travelling horizontally at 2.5 m/s hits and stick to the very bottom tip of the rod. To what maximum angle, measured from vertical, does the rod rotates when the ball of clay is attached to the rod? just how to approach for the problem

Answer 1

So I guess that that is how the problem is set up.

This seems like a problem concerning the transfer of momentum.
The ball has a momentum, which is the product of it's velocity and mass.
The rod has no momentum, because it has no velocity.
Momentum must be the same before and after.

So you want to look at the momentum before and after the collision.

Angular momentum for the rod with a axis at the center is\[\frac{1}{12}Ml^2 \omega\]\[l\text{ is length overall and } \omega\text{ is angular velocity}\] http://hyperphysics.phy-astr.gsu.edu/hbase/amom.html#am
http://hyperphysics.phy-astr.gsu.edu/hbase/mi2.html#irod

For the ball, we consider it to be a point, rotating. We don't have information on it's dimensions to get specific anyway. When attached to the stick, it's angular momentum is\[mr^2\omega\]

The sum of the two would be the total angular momentum, and thus the total momentum (because there is no linear momentum).

Now you can find the initial angular velocity of the rod-and-ball.